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

1,4

Links

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

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A028598 A272618 A265397 * A071326 A284103 A151674

Adjacent sequences: A071324 A071325 A071326 * A071328 A071329 A071330

Keyword

nonn

Author

Reinhard Zumkeller, May 18 2002

Status

approved