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%I #13 Feb 09 2020 20:12:25
%S 1,3,7,4,31,15,511,12,13,63,131071,28,8589934591,1023,127,6,
%T 36893488147419103231,39,680564733841876926926749214863536422911,124,
%U 2047,262143,231584178474632390847141970017375815706539969331281128078915168015826259279871,60,121,17179869183,91,2044
%N a(n) = sigma(A225546(n)), where sigma is the sum of divisors.
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = A000203(A225546(n)).
%F For all n >= 1, A000035(a(A016754(n))) = 1. [Result is odd for all odd squares]
%t Array[If[# == 1, 1, DivisorSigma[1, #] &@ Apply[Times, Flatten@ Map[Function[{p, e}, Map[Prime[Log2@ # + 1]^(2^(PrimePi@ p - 1)) &, DeleteCases[NumberExpand[e, 2], 0]]] @@ # &, FactorInteger[#]]]] &, 28] (* _Michael De Vlieger_, Feb 08 2020 *)
%o (PARI)
%o A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
%o A331733(n) = if(1==n,1,my(f=factor(n),u=#binary(vecmax(f[, 2])),prods=vector(u,x,1),m=1,e); for(i=1,u,for(k=1,#f~, if(bitand(f[k,2],m),prods[i] *= f[k,1])); m<<=1); prod(i=1,u,(prime(i)^(1+A048675(prods[i]))-1)/(prime(i)-1)));
%Y Cf. A000203, A048675, A225546, A331309, A331734, A331735, A331741.
%Y Cf. A323243, A323173, A324054, A324184, A324545 for other permutations of sigma, and also A324573, A324653.
%K nonn
%O 1,2
%A _Antti Karttunen_, Feb 02 2020
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