A373224 Row sums of A373223.

0, 1, 2, 1, 0, 5, 6, 1, 0, 9, 0, 11, 12, 1, 0, 15, 0, 17, 0, -1, 20, -1, -2, 23, 24, 25, 0, -1, 28, 29, 0, -1, 32, -1, 34, -1, 36, -1, -2, 39, -2, 41, -2, 43, 44, -1, -2, -3, -4, 49, 50, -3, 52, -3, 54, -3, 56, -3, 58, 59, -2, 61, -2, -3, 64, 65, -2, 67, -2, 69, 70, -1, -2

Offset: 1

Author

Peter Luschny, May 28 2024

Keywords

• sign

Crossrefs

Cf. A373223, A373225, A002144, A080147.

Programs

Maple

A373224 := n -> local k; add(A373223(n, k), k = 1..n):
lprint(seq(A373224(n), n  = 1..73));

PARI

KP(p,q) = kronecker(p,q);
T(n,k) =  my(p=prime(n), q=prime(k)); KP(p,q) * KP(q,p);
a(n) = vecsum(vector(n, k, T(n,k))); \\ Michel Marcus, May 30 2024

Formula

a(k) = k - 1 <==> k = 1 or 2 or k term of A080147. In other words: If we index the primes starting at 0 then 0, 1 and the indices of the Pythagorean primes (A002144) are the fixed points of this map.