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

Asa(n) = A048673(A249823(n)), as a composition of related permutations:.

aA007310(n) = A048673A249735(A249823a(n)) for all n)). >= 1. (This is the permutation which sorts the terms of A249735 into an ascending order, as they occur in A007310.)

Other identities. For all n >= 1:

A007310(n) = A249735(a(n)). [This is the permutation which sorts the terms of A249735 into an ascending order, as they occur in A007310.]

(PARI) A249745(n)=(1+)=A064989(A007310(n)))/))\2+1 \\ M. F. Hasler, Jan 19 2016

(PARI) A249745(n)=(1+A064989(A007310(n)))/2 \\ M. F. Hasler, Jan 19 2016

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a249745[n_Integer] := Module[{f, p, a064989, a007310, a},

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

p[x_] := Which[

x == 1, 1,

x == 2, 1,

True, NextPrime[x, -1]];

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

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

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

a[n]]; a249745[252] (* Michael De Vlieger, Dec 18 2014, after Harvey P. Dale at A007310 *)

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Michael De Vlieger: Added mma, sorry hadn't added it before approval.

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