A378546 a(n) is the sum of the divisors d of n for which A083345(n/d) is even, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).

1, 2, 3, 4, 5, 6, 7, 8, 10, 10, 11, 13, 13, 14, 16, 17, 17, 20, 19, 21, 22, 22, 23, 26, 26, 26, 30, 29, 29, 32, 31, 34, 34, 34, 36, 43, 37, 38, 40, 42, 41, 44, 43, 45, 53, 46, 47, 55, 50, 52, 52, 53, 53, 60, 56, 58, 58, 58, 59, 72, 61, 62, 73, 68, 66, 68, 67, 69, 70, 72, 71, 86, 73, 74, 83, 77, 78, 80, 79, 89, 91

Offset: 1

Author

Antti Karttunen, Nov 30 2024

Keywords

• nonn

Comments

Dirichlet convolution of A000027 with A369001.

Dirichlet convolution of A000010 (Euler phi) with A378444.

Links

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

Crossrefs

Cf. A000010, A000027, A000203, A083345, A369001, A378444, A378547.

Cf. also A378544, A378545.

Programs

PARI

A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369001(n) = !(A083345(n)%2);
A378546(n) = sumdiv(n,d,d*A369001(n/d));

Formula

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

a(n) = Sum_{d|n} A000010(n/d)*A378444(d).

a(n) = A000203(n) - A378547(n).