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
Keywords
Links
- Antti Karttunen, Table of n, a(n) for n = 1..65537
Programs
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Mathematica
Array[DivisorSum[#, # &, PrimeQ@ Sqrt@ # &] &, 91] (* Michael De Vlieger, Nov 18 2017 *)
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PARI
A071327(n) = { my(r); sumdiv(n,d,(issquare(d,&r)&&isprime(r)) * d); } \\ Antti Karttunen, Nov 19 2017
Formula
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