A378545 a(n) is the sum of those divisors d of n for which A083345(d) is odd, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).

0, 2, 3, 6, 5, 11, 7, 14, 3, 17, 11, 15, 13, 23, 8, 14, 17, 29, 19, 21, 10, 35, 23, 47, 5, 41, 30, 27, 29, 56, 31, 46, 14, 53, 12, 69, 37, 59, 16, 69, 41, 74, 43, 39, 53, 71, 47, 95, 7, 67, 20, 45, 53, 110, 16, 91, 22, 89, 59, 120, 61, 95, 73, 110, 18, 110, 67, 57, 26, 108, 71, 173, 73, 113, 83, 63, 18, 128, 79, 149

Offset: 1

Author

Antti Karttunen, Nov 29 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A000203, A377874, A378544.

Cf. also A378445 (number of such divisors).

Programs

PARI

A377874(n) = { my(f=factor(n)); (numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1])))%2); };
A378545(n) = sumdiv(n,d,d*A377874(d));

Formula

a(n) = Sum_{d|n} d*A377874(d).

a(n) = A000203(n) - A378544(n).