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

1,1

Links

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

Formula

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

Prog

(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

Crossrefs

Cf. A000040.

Sequence in context: A301229 A365620 A301011 * A301221 A057317 A008068

Adjacent sequences: A034693 A034694 A034695 * A034697 A034698 A034699

Keyword

nonn

Author

N. J. A. Sloane

Status

approved