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A360996
Multiplicative with a(p^e) = 5*e, p prime and e > 0.
2
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
1,2
FORMULA
Dirichlet g.f.: Product_{primes p} (1 + 5*p^s/(p^s - 1)^2).
a(n) = A005361(n) * A082476(n).
MATHEMATICA
g[p_, e_] := 5*e; a[1] = 1; a[n_] := Times @@ g @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1+3*X+X^2)/(1-X)^2)[n], ", "))
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.
Sequence in context: A040021 A339720 A341831 * A003882 A168284 A166598
KEYWORD
nonn,mult
AUTHOR
Vaclav Kotesovec, Feb 28 2023
STATUS
approved