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A091399
a(n) = Product_{ p | n } (1 + Legendre(7,p) ).
3
1, 2, 2, 2, 0, 4, 1, 2, 2, 0, 0, 4, 0, 2, 0, 2, 0, 4, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 4, 2, 4, 0, 0, 0, 4, 0, 0, 0, 0, 2, 4, 1, 0, 0, 0, 2, 4, 0, 2, 4, 4, 2, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0
OFFSET
1,2
LINKS
FORMULA
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 7*sqrt(7) * log(8+3*sqrt(7))/(4*Pi^2) = 1.298843... . - 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, 7), n=1..120)];
MATHEMATICA
a[1] = 1; a[n_] := Product[1+JacobiSymbol[7, p], {p, FactorInteger[n][[All, 1]]}];
Array[a, 105] (* Jean-François Alcover, Aug 26 2019 *)
PROG
(PARI) a(n)={my(f=factor(n)[, 1]); prod(i=1, #f, 1 + kronecker(7, f[i]))} \\ Andrew Howroyd, Jul 23 2018
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
N. J. A. Sloane, Mar 02 2004
STATUS
approved