A372725 a(n) = Sum_{k=2..n+2} L(n/prime(k)) where L(n/p) is the Legendre symbol. Row sums of A372726.

0, 2, -1, -1, 5, -3, -2, -3, -3, 9, -2, -3, -4, -3, -2, -2, 17, -3, -4, -1, -2, 0, -4, -1, 0, 25, -4, -1, -4, -5, -3, -5, -3, -6, -2, 2, 36, -1, 6, -4, -6, -7, 1, -3, -4, -2, 0, 9, -4, 49, -4, -4, -4, -7, -6, -4, -2, -6, -4, -3, 1, 1, 12, -4, 65, -2, -5, -5

Offset: 0

Author

Peter Luschny, May 22 2024

Keywords

• sign

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A372726, A372724 (fixed points).

Programs

Maple

L := (n, k) -> NumberTheory:-LegendreSymbol(n, ithprime(k)):
seq(add(L(n, k), k = 2..n + 2), n = 0..67);

Mathematica

A372725[n_] := Sum[JacobiSymbol[n, Prime[k]], {k, 2, n + 2}];
Array[A372725, 100, 0] (* Paolo Xausa, Jul 10 2024 *)

PARI

a(n) = sum(k=2, n+2, kronecker(n, prime(k))); \\ Michel Marcus, May 22 2024