A091394 - OEIS

A091394

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

1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4

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OFFSET

1,3

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)/(6*Pi) = 0.593135 . - 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 25 2018

CROSSREFS

Cf. A091379, A226162.

Sequence in context: A139366 A049767 A286351 * A029881 A347290 A070090

Adjacent sequences: A091391 A091392 A091393 * A091395 A091396 A091397

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Mar 02 2004

STATUS

approved