A347133 a(n) = Sum_{d|n} A003415(n/d) * A069359(d).

0, 0, 0, 1, 0, 2, 0, 6, 1, 2, 0, 16, 0, 2, 2, 24, 0, 19, 0, 20, 2, 2, 0, 72, 1, 2, 9, 24, 0, 40, 0, 80, 2, 2, 2, 111, 0, 2, 2, 96, 0, 48, 0, 32, 25, 2, 0, 256, 1, 29, 2, 36, 0, 117, 2, 120, 2, 2, 0, 244, 0, 2, 29, 240, 2, 64, 0, 44, 2, 56, 0, 446, 0, 2, 31, 48, 2, 72, 0, 352, 54, 2, 0, 308, 2, 2, 2, 168, 0, 304, 2, 56

Offset

1,6

Comments

Dirichlet convolution of A003415 (arithmetic derivative) with A069359.

Dirichlet convolution of A001221 (omega, number of distinct prime factors of n) with A347131.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10080

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

a(n) = Sum_{d|n} A003415(n/d) * A069359(d).

a(n) = Sum_{d|n} A001221(n/d) * A347131(d).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A069359(n) = (n*sumdiv(n, d, isprime(d)/d)); \\ From A069359
A347133(n) = sumdiv(n, d, A003415(n/d)*A069359(d));

Crossrefs

Cf. A001221, A003415, A069359, A347131.

Cf. also A300251, A305809, A347132, A347134, A347135.

Sequence in context: A330609 A180047 A180397 * A317842 A021489 A092158

Adjacent sequences: A347130 A347131 A347132 * A347134 A347135 A347136

Keyword

nonn

Author

Antti Karttunen, Aug 23 2021

Status

approved