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A226569 Inverse permutation to A226532.

%I A226569 #11 Aug 21 2025 19:47:49
%S A226569 1,2,6,4,15,3,35,8,36,30,77,24,143,70,10,16,221,72,323,60,210,154,437,
%T A226569 12,225,286,216,140,667,5,899,32,462,442,21,9,1147,646,858,120,1517,
%U A226569 105,1763,308,540,874,2021,96,1225,450,1326,572,2491,108,1155,280
%N A226569 Inverse permutation to A226532.
%H A226569 Robert Israel, <a href="/A226569/b226569.txt">Table of n, a(n) for n = 1..10000</a>
%H A226569 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A226569 If k = Prod_{i=1..m} prime(i)^e(i), then a(k) = prime(m)^e(m) * Prod_{i=1..m-1} prime(i)^(e(i) xor e(i+1)). - _Robert Israel_, Aug 21 2025
%p A226569 f:= proc(n) local F,Fp,V,m,j,r;
%p A226569   F:= ifactors(n)[2];
%p A226569   Fp:= map(numtheory:-pi, F[..,1]);
%p A226569   m:= max(Fp);
%p A226569   V:= Vector(m);
%p A226569   for j from 1 to nops(F) do V[Fp[j]]:= F[j,2] od:
%p A226569   r:= ithprime(m)^V[m];
%p A226569   for j from m-1 to 1 by -1 do r:= r * ithprime(j)^Bits:-Xor(V[j],V[j+1]) od;
%p A226569   r
%p A226569 end proc:
%p A226569 f(1):= 1:
%p A226569 map(f, [$1..100]); # _Robert Israel_, Aug 21 2025
%o A226569 (Haskell)
%o A226569 -- import Data.List (elemIndex); import Data.Maybe (fromJust)
%o A226569 a226569 = (+ 1) . fromJust . (`elemIndex` a226532_list)
%Y A226569 Cf. A000079 (fixed points).
%K A226569 nonn,look
%O A226569 1,2
%A A226569 _Reinhard Zumkeller_, Jun 11 2013