A360996 Multiplicative with a(p^e) = 5*e, p prime and e > 0.

1, 5, 5, 10, 5, 25, 5, 15, 10, 25, 5, 50, 5, 25, 25, 20, 5, 50, 5, 50, 25, 25, 5, 75, 10, 25, 15, 50, 5, 125, 5, 25, 25, 25, 25, 100, 5, 25, 25, 75, 5, 125, 5, 50, 50, 25, 5, 100, 10, 50, 25, 50, 5, 75, 25, 75, 25, 25, 5, 250, 5, 25, 50, 30, 25, 125, 5, 50, 25, 125, 5, 150

Offset: 1

Author

Vaclav Kotesovec, Feb 28 2023

Keywords

• nonn
• mult
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005361 (multiplicative with a(p^e) = e), A000005 (e+1), A343443 (e+2), A360997 (e+3), A322327 (2*e), A048691 (2*e+1), A360908 (2*e-1), A226602 (3*e), A048785 (3*e+1), A360910 (3*e-1), A360909 (3*e+2), A360911 (3*e-2), A322328 (4*e).

Cf. A082476.

Programs

Mathematica

g[p_, e_] := 5*e; a[1] = 1; a[n_] := Times @@ g @@@ FactorInteger[n]; Array[a, 100]

PARI

for(n=1, 100, print1(direuler(p=2, n, (1+3*X+X^2)/(1-X)^2)[n], ", "))

Formula

Dirichlet g.f.: Product_{primes p} (1 + 5*p^s/(p^s - 1)^2).

a(n) = A005361(n) * A082476(n).