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A249745 Permutation of natural numbers: a(n) = (1 + A064989(A007310(n))) / 2.

%I A249745 #21 Jan 19 2016 22:10:37
%S A249745 1,2,3,4,6,7,9,10,5,12,15,8,16,19,21,22,13,24,11,27,30,17,31,34,36,18,
%T A249745 37,40,20,42,28,26,45,49,51,52,54,55,29,33,25,14,57,64,43,66,69,39,35,
%U A249745 70,75,44,76,48,79,82,61,84,23,87,90,47,46,91,96,97,99,58,56,60,100,62,73,72,106,112,114,115,65,117,120,38,94,121
%N A249745 Permutation of natural numbers: a(n) = (1 + A064989(A007310(n))) / 2.
%H A249745 Antti Karttunen, <a href="/A249745/b249745.txt">Table of n, a(n) for n = 1..10000</a>
%H A249745 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A249745 a(n) = (A064989(A007310(n)) + 1) / 2.
%F A249745 a(n) = A048673(A249823(n)), as a composition of related permutations.
%F A249745 A007310(n) = A249735(a(n)) for all n >= 1. (This is the permutation which sorts the terms of A249735 into an ascending order, as they occur in A007310.)
%t A249745 a249745[n_Integer] := Module[{f, p, a064989, a007310, a},
%t A249745   f[x_] := Transpose@FactorInteger[x];
%t A249745   p[x_] := Which[
%t A249745     x == 1, 1,
%t A249745     x == 2, 1,
%t A249745     True, NextPrime[x, -1]];
%t A249745   a064989[x_] := Times @@ Power[p /@ First[f[x]], Last[f[x]]];
%t A249745   a007310[x_] := Select[Range[x], MemberQ[{1, 5}, Mod[#, 6]] &];
%t A249745   a[x_] := (1 + a064989 /@ a007310[x])/2;
%t A249745 a[n]]; a249745[252] (* _Michael De Vlieger_, Dec 18 2014, after _Harvey P. Dale_ at A007310 *)
%o A249745 (Scheme) (define (A249745 n) (/ (+ 1 (A064989 (A007310 n))) 2))
%o A249745 (PARI) A249745(n)=A064989(A007310(n))\2+1 \\ _M. F. Hasler_, Jan 19 2016
%Y A249745 Inverse: A249746.
%Y A249745 Row 2 of A251721.
%Y A249745 Cf. A007310, A048673, A064989, A249823, A249735.
%K A249745 nonn
%O A249745 1,2
%A A249745 _Antti Karttunen_, Nov 23 2014