A071327 - OEIS

%I #25 Feb 21 2022 11:20:08

%S 0,0,0,4,0,0,0,4,9,0,0,4,0,0,0,4,0,9,0,4,0,0,0,4,25,0,9,4,0,0,0,4,0,0,

%T 0,13,0,0,0,4,0,0,0,4,9,0,0,4,49,25,0,4,0,9,0,4,0,0,0,4,0,0,9,4,0,0,0,

%U 4,0,0,0,13,0,0,25,4,0,0,0,4,9,0,0,4,0,0,0,4,0,9,0

%N Sum of the squared primes dividing n.

%H Antti Karttunen, <a href="/A071327/b071327.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = Sum_{d|n} A010052(d)*A010051(A000196(d))*d. - _Antti Karttunen_, Nov 18 2017

%F G.f.: Sum_{k>=1} prime(k)^2 * x^(prime(k)^2) / (1 - x^(prime(k)^2)). - _Ilya Gutkovskiy_, Apr 06 2020

%F a(n) = Sum_{p^2|n} p^2. - _Wesley Ivan Hurt_, Feb 21 2022

%t Array[DivisorSum[#, # &, PrimeQ@ Sqrt@ # &] &, 91] (* _Michael De Vlieger_, Nov 18 2017 *)

%o (PARI) A071327(n) = { my(r); sumdiv(n,d,(issquare(d,&r)&&isprime(r)) * d); } \\ _Antti Karttunen_, Nov 19 2017

%Y Cf. A010051, A010052, A063958, A056170, A071326.

%K nonn

%O 1,4

%A _Reinhard Zumkeller_, May 18 2002