A324891 a(n) = sigma(A170818(n)), where A170818(n) is the part of n composed of prime factors of form 4k+1.

1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 14, 1, 6, 1, 18, 1, 1, 6, 1, 1, 1, 1, 31, 14, 1, 1, 30, 6, 1, 1, 1, 18, 6, 1, 38, 1, 14, 6, 42, 1, 1, 1, 6, 1, 1, 1, 1, 31, 18, 14, 54, 1, 6, 1, 1, 30, 1, 6, 62, 1, 1, 1, 84, 1, 1, 18, 1, 6, 1, 1, 74, 38, 31, 1, 1, 14, 1, 6, 1, 42, 1, 1, 108, 1, 30, 1, 90, 6, 14, 1, 1, 1, 6, 1, 98, 1, 1, 31, 102, 18, 1, 14, 6

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, A170818, A324893.

Programs

PARI

A324891(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4>1, 1, ((f[i,1]^(1+f[i,2]))-1)/(f[i,1]-1))); };

PARI

A170818(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4>1, 1, f[i, 1])^f[i, 2]); }; \\ From A170818
A324891(n) = sigma(A170818(n));

Formula

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

a(n) = A000203(A170818(n)).

a(n) = A000593(n) / A324893(n).