A358780 Dirichlet g.f.: zeta(s) * zeta(2*s) * zeta(3*s) * zeta(4*s).

1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 5, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 6, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 5, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 9, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 2, 2, 1, 1, 1, 5, 5, 1, 1, 2, 1, 1, 1, 3

Offset: 1

Author

Vaclav Kotesovec, Mar 14 2023

Keywords

• nonn
• mult

Comments

a(n) = A000688(n) for n < 32.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046951, A322885, A000688.

Cf. A001400, A063966.

Programs

PARI

for(n=1, 200, print1(direuler(p=2, n, 1/(1 - X)/(1 - X^2)/(1 - X^3)/(1 - X^4))[n], ", "))

Formula

Multiplicative with a(p^e) = A001400(e).

Sum_{k=1..n} a(k) ~ Pi^6*zeta(3)*n/540 + Pi^2*zeta(1/2)*zeta(3/2)*sqrt(n)/6 + zeta(1/3)*zeta(2/3)*zeta(4/3)*n^(1/3) + zeta(1/4)*zeta(1/2)*zeta(3/4)*n^(1/4).