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A091394 a(n) = Product_{ p | n } (1 + Legendre(-5,p) ). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
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
Sequence in context: A139366 A049767 A286351 * A029881 A347290 A070090
KEYWORD
nonn,mult
AUTHOR
N. J. A. Sloane, Mar 02 2004
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)