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A266645 Permutation of natural numbers: a(n) = A064989(A250469(n)).

%I A266645 #15 Mar 09 2017 10:40:04
%S A266645 1,2,3,4,5,6,7,10,9,8,11,14,13,22,15,12,17,26,19,34,21,20,23,38,25,18,
%T A266645 33,16,29,46,31,58,39,28,35,30,37,62,51,44,41,74,43,82,57,24,47,86,49,
%U A266645 50,27,52,53,94,55,42,69,68,59,106,61,118,87,40,65,66,67,122,45,76,71,134,73,142,93,36,77,70,79,146,111,32,83,158,85,78,123
%N A266645 Permutation of natural numbers: a(n) = A064989(A250469(n)).
%H A266645 Antti Karttunen, <a href="/A266645/b266645.txt">Table of n, a(n) for n = 1..10000</a>
%H A266645 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A266645 a(n) = A064989(A250469(n)).
%F A266645 a(n) = A064989(A249817(A003961(A249818(n)))).
%F A266645 As a composition of related permutations:
%F A266645 a(n) = A266416(A266403(n)).
%F A266645 Other identities. For all n >= 0:
%F A266645 A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]
%F A266645 A020639(a(n)) = A020639(n). [More generally, it preserves the smallest prime dividing n.]
%F A266645 A055396(a(n)) = A055396(n).
%t A266645 f[n_] := Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n; g[n_] := If[n == 1, 0, PrimePi@ FactorInteger[n][[1, 1]]]; Function[s, MapIndexed[ Function[{m, n}, f[Lookup[s, g[n] + 1][[m]] - Boole[n == 1]]][#1, First@ #2] &, #] &@ Map[Position[Lookup[s, g@ #], #][[1, 1]] &, Range@ 120]]@ PositionIndex@ Array[g, 10^4] (* _Michael De Vlieger_, Mar 09 2017, Version 10 *)
%o A266645 (Scheme, two alternatives)
%o A266645 (define (A266645 n) (A064989 (A250469 n)))
%o A266645 (define (A266645 n) (A064989 (A249817 (A003961 (A249818 n)))))
%Y A266645 Inverse: A266646.
%Y A266645 Cf. A000035, A003961, A020639, A055396, A064989, A250469.
%Y A266645 Related permutations: A266403, A266416, A249817, A249818.
%K A266645 nonn
%O A266645 1,2
%A A266645 _Antti Karttunen_, Jan 02 2016