A338768 Sum of the remainders (p*q mod n) with p,q prime, p + q = n and p <= q.

0, 0, 0, 0, 1, 3, 3, 7, 5, 6, 0, 11, 9, 12, 11, 14, 0, 16, 15, 22, 17, 43, 0, 69, 21, 33, 0, 22, 0, 51, 27, 46, 29, 66, 0, 80, 0, 46, 35, 101, 0, 80, 39, 81, 41, 114, 0, 163, 45, 112, 0, 105, 0, 139, 51, 133, 0, 116, 0, 162, 57, 95, 59, 179, 0, 204, 0, 78, 65, 241, 0, 258, 69, 181

Offset: 1

Author

Wesley Ivan Hurt, Nov 07 2020

Keywords

• nonn

Examples

			a(16) = 14; (3*13 mod 16) + (5*11 mod 16) = 7 + 7 = 14.
		

Crossrefs

Cf. A010051, A338769.

Programs

Mathematica

Table[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]) Mod[i (n - i), n], {i, Floor[n/2]}], {n, 80}]

Formula

a(n) = Sum_{i=1..floor(n/2)} ( i*(n-i) mod n ) * c(i) * c(n-i), where c is the prime characteristic (A010051).