cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A034696 Dirichlet convolution of primes (A000040) with themselves.

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%I A034696 #19 Jun 22 2024 11:54:11
%S A034696 4,12,20,37,44,82,68,118,117,182,124,296,164,274,298,375,236,512,268,
%T A034696 612,462,502,332,950,509,650,642,924,436,1310,508,1108,858,910,970,
%U A034696 1831,628,1054,1078,1942,716,2034,764,1680,1764,1294,844,2968,1197,2136,1522
%N A034696 Dirichlet convolution of primes (A000040) with themselves.
%H A034696 Seiichi Manyama, <a href="/A034696/b034696.txt">Table of n, a(n) for n = 1..10000</a>
%F A034696 a(n) = Sum_{d|n} prime(d)*prime(n/d). - _Ilya Gutkovskiy_, Mar 11 2018
%t A034696 Table[DivisorSum[n, Prime[n/#]*Prime[#] &], {n, 80}] (* _Wesley Ivan Hurt_, Jun 22 2024 *)
%o A034696 (PARI) a(n) = sumdiv(n, d, prime(d)*prime(n/d)); \\ _Michel Marcus_, Mar 11 2018
%o A034696 (Python)
%o A034696 from sympy import divisors, prime, primerange
%o A034696 def dirichlet(f, g, n): return sum(f[d] * g[n//d] for d in divisors(n))
%o A034696 def aupton(terms):
%o A034696   p = [0] + list(primerange(2, prime(terms)+1))
%o A034696   return [dirichlet(p, p, k) for k in range(1, terms+1)]
%o A034696 print(aupton(51)) # _Michael S. Branicky_, Apr 12 2021
%Y A034696 Cf. A000040.
%K A034696 nonn
%O A034696 1,1
%A A034696 _N. J. A. Sloane_