OFFSET
1,2
COMMENTS
Multiplicative because the Moebius transform of a multiplicative sequence is multiplicative. - Andrew Howroyd, Jul 25 2018
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Enrique Pérez Herrero)
FORMULA
Dirichlet g.f.: 1/zeta(s)^4.
Multiplicative with a(p^e) = (-1)^e * binomial(4, e). - Amiram Eldar, Sep 11 2020
MATHEMATICA
tau[1, n_Integer]:=1; SetAttributes[tau, Listable];
tau[k_Integer, n_Integer]:=Plus@@(tau[k-1, Divisors[n]])/; k > 1;
tau[k_Integer, n_Integer]:=Plus@@(tau[k+1, Divisors[n]]*MoebiusMu[n/Divisors[n]]); k<1;
Table[tau[-4, n], {n, 70}]
f[p_, e_] := (-1)^e * Binomial[4, e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 11 2020 *)
PROG
(PARI) seq(n)={my(v=vector(n, n, n==1)); for(k=1, 4, v=dirmul(v, vector(#v, n, moebius(n)))); v} \\ Andrew Howroyd, Jul 25 2018
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - X)^4)[n], ", ")) \\ Vaclav Kotesovec, Feb 22 2021
CROSSREFS
KEYWORD
sign,mult,easy
AUTHOR
Enrique Pérez Herrero, Sep 14 2014
STATUS
approved