|
|
A360970
|
|
Multiplicative with a(p^e) = e^3, p prime and e > 0.
|
|
4
|
|
|
1, 1, 1, 8, 1, 1, 1, 27, 8, 1, 1, 8, 1, 1, 1, 64, 1, 8, 1, 8, 1, 1, 1, 27, 8, 1, 27, 8, 1, 1, 1, 125, 1, 1, 1, 64, 1, 1, 1, 27, 1, 1, 1, 8, 8, 1, 1, 64, 8, 8, 1, 8, 1, 27, 1, 27, 1, 1, 1, 8, 1, 1, 8, 216, 1, 1, 1, 8, 1, 1, 1, 216, 1, 1, 8, 8, 1, 1, 1, 64, 64
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
LINKS
|
|
|
FORMULA
|
Dirichlet g.f.: zeta(s) * Product_{primes p} (1 + (7*p^(2*s) - 2*p^s + 1) / (p^s*(p^s - 1)^3)).
Sum_{k=1..n} a(k) ~ c * n, where c = Product_{primes p} (1 + (7*p^2 - 2*p + 1) / (p*(p-1)^3)) = 109.601930729008995813857898403091253809628920963774227252953...
|
|
MAPLE
|
f:= proc(n) local t;
mul(t^3, t = ifactors(n)[2][.., 2]);
end proc:
|
|
MATHEMATICA
|
g[p_, e_] := e^3; 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 + 10*X^2 - 3*X^3 + X^4)/(1-X)^4)[n], ", "))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|