A034696 Dirichlet convolution of primes (A000040) with themselves.

4, 12, 20, 37, 44, 82, 68, 118, 117, 182, 124, 296, 164, 274, 298, 375, 236, 512, 268, 612, 462, 502, 332, 950, 509, 650, 642, 924, 436, 1310, 508, 1108, 858, 910, 970, 1831, 628, 1054, 1078, 1942, 716, 2034, 764, 1680, 1764, 1294, 844, 2968, 1197, 2136, 1522

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040.

Programs

Mathematica

Table[DivisorSum[n, Prime[n/#]*Prime[#] &], {n, 80}] (* Wesley Ivan Hurt, Jun 22 2024 *)

PARI

a(n) = sumdiv(n, d, prime(d)*prime(n/d)); \\ Michel Marcus, Mar 11 2018

Python

from sympy import divisors, prime, primerange
def dirichlet(f, g, n): return sum(f[d] * g[n//d] for d in divisors(n))
def aupton(terms):
  p = [0] + list(primerange(2, prime(terms)+1))
  return [dirichlet(p, p, k) for k in range(1, terms+1)]
print(aupton(51)) # Michael S. Branicky, Apr 12 2021

Formula

a(n) = Sum_{d|n} prime(d)*prime(n/d). - Ilya Gutkovskiy, Mar 11 2018