A034696 - OEIS

%I #19 Jun 22 2024 11:54:11

%S 4,12,20,37,44,82,68,118,117,182,124,296,164,274,298,375,236,512,268,

%T 612,462,502,332,950,509,650,642,924,436,1310,508,1108,858,910,970,

%U 1831,628,1054,1078,1942,716,2034,764,1680,1764,1294,844,2968,1197,2136,1522

%N Dirichlet convolution of primes (A000040) with themselves.

%H Seiichi Manyama, <a href="/A034696/b034696.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Sum_{d|n} prime(d)*prime(n/d). - _Ilya Gutkovskiy_, Mar 11 2018

%t Table[DivisorSum[n, Prime[n/#]*Prime[#] &], {n, 80}] (* _Wesley Ivan Hurt_, Jun 22 2024 *)

%o (PARI) a(n) = sumdiv(n, d, prime(d)*prime(n/d)); \\ _Michel Marcus_, Mar 11 2018

%o (Python)

%o from sympy import divisors, prime, primerange

%o def dirichlet(f, g, n): return sum(f[d] * g[n//d] for d in divisors(n))

%o def aupton(terms):

%o   p = [0] + list(primerange(2, prime(terms)+1))

%o   return [dirichlet(p, p, k) for k in range(1, terms+1)]

%o print(aupton(51)) # _Michael S. Branicky_, Apr 12 2021

%Y Cf. A000040.

%K nonn

%O 1,1

%A _N. J. A. Sloane_