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A247343 Moebius transform applied four times to sequence 1,0,0,0,.... 9
1, -4, -4, 6, -4, 16, -4, -4, 6, 16, -4, -24, -4, 16, 16, 1, -4, -24, -4, -24, 16, 16, -4, 16, 6, 16, -4, -24, -4, -64, -4, 0, 16, 16, 16, 36, -4, 16, 16, 16, -4, -64, -4, -24, -24, 16, -4, -4, 6, -24, 16, -24, -4, 16, 16, 16, 16, 16, -4, 96, -4, 16, -24, 0, 16, -64, -4, -24, 16, -64 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A205031 A339719 A276683 * A071256 A078240 A296844
KEYWORD
sign,mult,easy
AUTHOR
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)