Hmm, I botched slightly the %F-line definitions of A091202- A091205.
Here are the corrected ones:
(Only %F-lines changed from my previous mail, so just overwrite).

%I A091202
%S A091202 0,1,2,3,4,7,6,11,8,5,14,13,12,19,22,9,16,25,10,31,28,29,26,37,24,21,
%T A091202 38,15,44,41,18,47,32,23,50,49,20,55,62,53,56,59,58,61,52,27,74,67,48,
%U A091202 69,42,43,76,73,30,35,88,33,82,87,36,91,94,39,64,121,46,97,100,111,98
%N A091202 Factorization-preserving isomorphism from integers to GF(2)[X]-polynomials.
%F A091202 a(0)=0, a(1)=1, a(p_i) = A014580(i) for primes p_i with index i, and for composites a(p_i * p_j * ...) = a(p_i) X a(p_j) X ..., where X stands for carryless multiplication of GF(2)[X] polynomials (A048720).
%C A091202 E.g. we have the following identities: A000005(n) = A091220(a(n)), A001221(n) = A091221(a(n)), A001222(n) = A091222(a(n)), A008683(n) = A091219(a(n)), A014580(n) = a(A000040(n)), A049084(n) = A091227(a(n)).
%H A091202 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091202 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A091202 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%Y A091202 Inverse: A091203. Cf. A091204 for "deep" variant.
%K A091202 nonn
%O A091202 0,3
%A A091202 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004


%I A091203
%S A091203 0,1,2,3,4,9,6,5,8,15,18,7,12,11,10,27,16,81,30,13,36,25,14,33,24,17,
%T A091203 22,45,20,21,54,19,32,57,162,55,60,23,26,63,72,29,50,51,28,135,66,31,
%U A091203 48,35,34,243,44,39,90,37,40,99,42,41,108,43,38,75,64,225,114,47,324
%N A091203 Factorization-preserving isomorphism from GF(2)[X]-polynomials to integers.
%F A091203 a(0)=0, a(1)=1. For n's coding an irreducible polynomial ir_i, that is if n=A014580(i), we have a(n) = A000040(i), and for composite polynomials a(ir_i X ir_j X ...) = p_i * p_j * ..., where p_i = A000040(i) and X stands for carryless multiplication of GF(2)[X] polynomials (A048720), and * for the ordinary multiplication of integers (A004247).
%C A091203 E.g. we have the following identities: A000040(n) = a(A014580(n)), A091219(n) = A008683(a(n)), A091220(n) = A000005(a(n)), A091221(n) = A001221(a(n)), A091222(n) = A001222(a(n)), A091225(n) = A010051(a(n)), A091227(n) = A049084(a(n)), A091247(n) = A066247(a(n)).
%H A091203 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091203 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A091203 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%Y A091203 Inverse: A091202. Cf. A091205 for "deep" variant.
%K A091203 nonn
%O A091203 0,3
%A A091203 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004


%I A091204
%S A091204 0,1,2,3,4,7,6,11,8,5,14,25,12,19,22,9,16,47,10,31,28,29,50,13,24,21,
%T A091204 38,15,44,61,18,137,32,43,94,49,20,55,62,53,56,97,58,115,100,27,26,37,
%U A091204 48,69,42,113,76,73,30,79,88,33,122,319,36,41,274,39,64,121,86,185
%N A091204 Deep multiplicative isomorphism from integers to GF(2)[X]-polynomials.
%F A091204 a(0)=0, a(1)=1, a(p_i) = A014580(a(i)) for primes with index i, and for composites a(p_i * p_j * ...) = a(p_i) X a(p_j) X ..., where X stands for carryless multiplication of GF(2)[X] polynomials (A048720).
%C A091204 This isomorphism can be used in most cases where mere A091202 would work, but in addition this preserves also the structures where we recurse on prime's index. E.g. we have: A091230(n) = a(A007097(n)) and A061775(n) = A091238(a(n)). This is possible because the permutation contains an image of itself in its restriction to primes, i.e. a(n) = A091227(a(A000040(n))).
%H A091204 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091204 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A091204 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%Y A091204 Inverse: A091205.
%K A091204 nonn,nice
%O A091204 0,3
%A A091204 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091205
%S A091205 0,1,2,3,4,9,6,5,8,15,18,7,12,23,10,27,16,81,30,13,36,25,14,69,24,11,
%T A091205 46,45,20,21,54,19,32,57,162,115,60,47,26,63,72,61,50,33,28,135,138,
%U A091205 17,48,35,22,243,92,39,90,37,40,207,42,83,108,29,38,75,64,225,114,103
%N A091205 Deep multiplicative isomorphism from GF(2)[X]-polynomials to integers.
%F A091205 a(0)=0, a(1)=1. For n's coding an irreducible polynomial, that is if n=A014580(i), we have a(n) = A000040(a(i)), and for reducible polynomials a(ir_i X ir_j X ...) = a(ir_i) * a(ir_j) * ..., where ir_i = A014580(i), X stands for carryless multiplication of GF(2)[X] polynomials (A048720), and * for the ordinary multiplication of integers (A004247).
%C A091205 This isomorphism can be used in most cases where mere A091203 would work, but in addition this preserves also the structures where we recurse on irreducible polynomial's A014580-index. E.g. we have: A091238(n) = A061775(a(n)). This is possible because the permutation contains an image of itself in its restriction to irreducible polynomials, i.e. a(n) = A049084(a(A014580(n))).
%H A091205 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091205 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A091205 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%Y A091205 Inverse: A091204.
%K A091205 nonn,nice
%O A091205 0,3
%A A091205 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004


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Yours,

Antti Karttunen