A071327 Sum of the squared primes dividing n.

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, 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, 4, 0, 0, 0, 13, 0, 0, 25, 4, 0, 0, 0, 4, 9, 0, 0, 4, 0, 0, 0, 4, 0, 9, 0

Offset: 1

Author

Reinhard Zumkeller, May 18 2002

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000196, A010051, A010052, A056170, A063958, A071326.

Programs

Mathematica

Array[DivisorSum[#, # &, PrimeQ@ Sqrt@ # &] &, 91] (* Michael De Vlieger, Nov 18 2017 *)

PARI

A071327(n) = { my(r); sumdiv(n,d,(issquare(d,&r)&&isprime(r)) * d); } \\ Antti Karttunen, Nov 19 2017

Formula

a(n) = Sum_{d|n} A010052(d)*A010051(A000196(d))*d. - Antti Karttunen, Nov 18 2017

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

a(n) = Sum_{p^2|n} p^2. - Wesley Ivan Hurt, Feb 21 2022

Additive with a(p^e) = p^2 if e >= 2, and 0 otherwise. - Amiram Eldar, May 15 2025