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A338768 Sum of the remainders (p*q mod n) with p,q prime, p + q = n and p <= q. 2

%I

%S 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,

%T 0,51,27,46,29,66,0,80,0,46,35,101,0,80,39,81,41,114,0,163,45,112,0,

%U 105,0,139,51,133,0,116,0,162,57,95,59,179,0,204,0,78,65,241,0,258,69,181

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

%F 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).

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

%t 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}]

%Y Cf. A010051, A338769.

%K nonn

%O 1,6

%A _Wesley Ivan Hurt_, Nov 07 2020

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Last modified January 22 05:19 EST 2022. Contains 350481 sequences. (Running on oeis4.)