%I #21 Jan 19 2016 22:10:37

%S 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 37,40,20,42,28,26,45,49,51,52,54,55,29,33,25,14,57,64,43,66,69,39,35,

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

%H Antti Karttunen, <a href="/A249745/b249745.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(n) = (A064989(A007310(n)) + 1) / 2.

%F a(n) = A048673(A249823(n)), as a composition of related permutations.

%F 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[n_Integer] := Module[{f, p, a064989, a007310, a},

%t f[x_] := Transpose@FactorInteger[x];

%t p[x_] := Which[

%t x == 1, 1,

%t x == 2, 1,

%t True, NextPrime[x, -1]];

%t a064989[x_] := Times @@ Power[p /@ First[f[x]], Last[f[x]]];

%t a007310[x_] := Select[Range[x], MemberQ[{1, 5}, Mod[#, 6]] &];

%t a[x_] := (1 + a064989 /@ a007310[x])/2;

%t a[n]]; a249745[252] (* _Michael De Vlieger_, Dec 18 2014, after _Harvey P. Dale_ at A007310 *)

%o (Scheme) (define (A249745 n) (/ (+ 1 (A064989 (A007310 n))) 2))

%o (PARI) A249745(n)=A064989(A007310(n))\2+1 \\ _M. F. Hasler_, Jan 19 2016

%Y Inverse: A249746.

%Y Row 2 of A251721.

%Y Cf. A007310, A048673, A064989, A249823, A249735.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 23 2014