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A071327
Sum of the squared primes dividing n.
3
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 18 2002
STATUS
approved