A378547 a(n) is the sum of the divisors d of n for which A083345(n/d) is odd, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).

0, 1, 1, 3, 1, 6, 1, 7, 3, 8, 1, 15, 1, 10, 8, 14, 1, 19, 1, 21, 10, 14, 1, 34, 5, 16, 10, 27, 1, 40, 1, 29, 14, 20, 12, 48, 1, 22, 16, 48, 1, 52, 1, 39, 25, 26, 1, 69, 7, 41, 20, 45, 1, 60, 16, 62, 22, 32, 1, 96, 1, 34, 31, 59, 18, 76, 1, 57, 26, 72, 1, 109, 1, 40, 41, 63, 18, 88, 1, 97, 30, 44, 1, 126, 22, 46, 32

Offset: 1

Author

Antti Karttunen, Nov 30 2024

Keywords

• nonn

Comments

Dirichlet convolution of A000027 with A377874.

Dirichlet convolution of A000010 (Euler phi) with A378445.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000010, A000027, A000203, A083345, A377874, A378445, A378546.

Cf. also A378544, A378545.

Programs

PARI

A377874(n) = { my(f=factor(n)); (numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1])))%2); };
A378547(n) = sumdiv(n,d,d*A377874(n/d));

Formula

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

a(n) = Sum_{d|n} A000010(n/d)*A378445(d).

a(n) = A000203(n) - A378546(n).