A324893 a(n) = sigma(A097706(n)), where A097706(n) is the part of n composed of prime factors of form 4k+3.

1, 1, 4, 1, 1, 4, 8, 1, 13, 1, 12, 4, 1, 8, 4, 1, 1, 13, 20, 1, 32, 12, 24, 4, 1, 1, 40, 8, 1, 4, 32, 1, 48, 1, 8, 13, 1, 20, 4, 1, 1, 32, 44, 12, 13, 24, 48, 4, 57, 1, 4, 1, 1, 40, 12, 8, 80, 1, 60, 4, 1, 32, 104, 1, 1, 48, 68, 1, 96, 8, 72, 13, 1, 1, 4, 20, 96, 4, 80, 1, 121, 1, 84, 32, 1, 44, 4, 12, 1, 13, 8, 24, 128, 48, 20, 4, 1, 57, 156, 1, 1, 4

Offset: 1

Author

Antti Karttunen, Mar 27 2019

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A000593, A097706, A324891.

Programs

Mathematica

Array[DivisorSigma[1, Times @@ Power @@@ Select[FactorInteger[#], Mod[#[[1]], 4] == 3 &]] &, 102] (* Michael De Vlieger, Mar 30 2019 *)

PARI

A324893(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4<3, 1, ((f[i,1]^(1+f[i,2]))-1)/(f[i,1]-1))); };

PARI

A097706(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4<3, 1, f[i, 1])^f[i, 2]); };
A324893(n) = sigma(A097706(n));

Formula

Multiplicative with a(p^e) = (p^(e+1) - 1)/(p-1) if p == 3 (mod 4), otherwise a(p^e) = 1.

a(n) = A000203(A097706(n)).

a(n) = A000593(n) / A324891(n).