A091398 a(n) = Product_{ p | n } (1 + Legendre(5,p) ).

1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0

Offset

1,11

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 5*sqrt(5) * log(phi)/(2*Pi^2) = 0.272559..., where phi is the golden ratio (A001622). - Amiram Eldar, Oct 17 2022

Maple

with(numtheory); L := proc(n, N) local i, t1, t2; t1 := ifactors(n)[2]; t2 := mul((1+legendre(N, t1[i][1])), i=1..nops(t1)); end; [seq(L(n, 5), n=1..120)];

Mathematica

a[n_] := Times @@ (1+KroneckerSymbol[5, #]& /@ FactorInteger[n][[All, 1]]);
Array[a, 105] (* Jean-François Alcover, Apr 08 2020 *)

Prog

(PARI) a(n)={my(f=factor(n)[, 1]); prod(i=1, #f, 1 + kronecker(5, f[i]))} \\ Andrew Howroyd, Jul 23 2018

Crossrefs

Cf. A001622, A080891, A091379, A091396.

Sequence in context: A087781 A181009 A270599 * A374175 A062103 A112314

Adjacent sequences: A091395 A091396 A091397 * A091399 A091400 A091401

Keyword

nonn,mult

Author

N. J. A. Sloane, Mar 02 2004

Status

approved