A378544 a(n) is the sum of those divisors d of n for which A083345(d) is even, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).

1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 13, 1, 1, 16, 17, 1, 10, 1, 21, 22, 1, 1, 13, 26, 1, 10, 29, 1, 16, 1, 17, 34, 1, 36, 22, 1, 1, 40, 21, 1, 22, 1, 45, 25, 1, 1, 29, 50, 26, 52, 53, 1, 10, 56, 29, 58, 1, 1, 48, 1, 1, 31, 17, 66, 34, 1, 69, 70, 36, 1, 22, 1, 1, 41, 77, 78, 40, 1, 37, 91, 1, 1, 62, 86, 1, 88, 45, 1, 25

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, A369001, A378545.

Cf. also A378444 (number of such divisors).

Programs

PARI

A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369001(n) = !(A083345(n)%2);
A378544(n) = sumdiv(n,d,d*A369001(d));

Formula

a(n) = Sum_{d|n} d*A369001(d).

a(n) = A000203(n) - A378545(n).