A331733 a(n) = sigma(A225546(n)), where sigma is the sum of divisors.

1, 3, 7, 4, 31, 15, 511, 12, 13, 63, 131071, 28, 8589934591, 1023, 127, 6, 36893488147419103231, 39, 680564733841876926926749214863536422911, 124, 2047, 262143, 231584178474632390847141970017375815706539969331281128078915168015826259279871, 60, 121, 17179869183, 91, 2044

Offset: 1

Author

Antti Karttunen, Feb 02 2020

Keywords

• nonn

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A048675, A225546, A331309, A331734, A331735, A331741.

Cf. A323243, A323173, A324054, A324184, A324545 for other permutations of sigma, and also A324573, A324653.

Programs

Mathematica

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 *)

PARI

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
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)));

Formula

a(n) = A000203(A225546(n)).

For all n >= 1, A000035(a(A016754(n))) = 1. [Result is odd for all odd squares]