VOOZH about

URL: https://oeis.org/A091397

⇱ A091397 - OEIS

login
A091397
a(n) = Product_{ p | n } (1 + Legendre(3,p) ).
3
1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0
OFFSET
1,11
LINKS
FORMULA
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3*sqrt(3) * log(2+sqrt(3)) / (2*Pi^2) = 0.346676... . - 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, 3), n=1..120)];
MATHEMATICA
a[n_] := Times@@ (1+KroneckerSymbol[3, #]& /@ 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(3, f[i]))} \\ Andrew Howroyd, Jul 23 2018
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
N. J. A. Sloane, Mar 02 2004
STATUS
approved