A079055 Numbers of prime pairs (p,q), p<=q, such that (p+q) divides n.

0, 0, 0, 1, 1, 1, 1, 2, 1, 3, 0, 3, 1, 3, 2, 4, 0, 4, 1, 6, 2, 3, 0, 7, 2, 4, 1, 6, 0, 8, 1, 6, 1, 4, 2, 10, 0, 3, 2, 10, 0, 9, 1, 7, 4, 4, 0, 14, 2, 8, 0, 8, 0, 9, 2, 10, 1, 4, 0, 18, 1, 4, 4, 11, 2, 11, 0, 7, 1, 11, 0, 20, 1, 5, 4, 9, 1, 13, 0, 16, 2, 5, 0, 21, 2, 6, 0, 12, 0, 21, 3, 9, 1, 5, 2, 23, 0, 7

Offset

1,8

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{d|n} A061358(d). - Robert Israel, Oct 17 2023

Maple

N:= 100: # for a(1)..a(N)
P:= select(isprime, [2, seq(i, i=3..N, 2)]): nP:= nops(P):
V:= Vector(N):
for i from 1 to nP do
  for j from i to nP do
    v:= P[i]+P[j];
    J:= [seq(t, t=v..N, v)];
    V[J]:= V[J] +~ 1
od od:
convert(V, list); # Robert Israel, Oct 17 2023

Prog

(PARI) a(n)=sum(i=1, n, sum(j=1, i, if(n%(prime(i)+prime(j)), 0, 1)))

Crossrefs

Cf. A061358.

Sequence in context: A364235 A146094 A098035 * A122170 A066029 A141198

Adjacent sequences: A079052 A079053 A079054 * A079056 A079057 A079058

Keyword

nonn,look

Author

Benoit Cloitre, Feb 02 2003

Status

approved