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A063958
Sum of the non-unitary prime divisors of n: sum of those prime divisors for which the exponent in the prime factorization exceeds 1.
7
0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 2, 0, 0, 0, 2, 0, 3, 0, 2, 0, 0, 0, 2, 5, 0, 3, 2, 0, 0, 0, 2, 0, 0, 0, 5, 0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 2, 7, 5, 0, 2, 0, 3, 0, 2, 0, 0, 0, 2, 0, 0, 3, 2, 0, 0, 0, 2, 0, 0, 0, 5, 0, 0, 5, 2, 0, 0, 0, 2, 3, 0, 0, 2, 0, 0, 0, 2, 0, 3, 0, 2, 0, 0, 0, 2, 0, 7, 3, 7, 0, 0, 0, 2, 0
OFFSET
1,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 1000 terms from Harry J. Smith)
FORMULA
G.f.: Sum_{k>=1} prime(k) * x^(prime(k)^2) / (1 - x^(prime(k)^2)). - Ilya Gutkovskiy, Apr 06 2020
a(n) = sopf(rad(n/rad(n))). - Wesley Ivan Hurt, Nov 21 2021
a(n) = Sum_{p^2|n} p. - Wesley Ivan Hurt, Feb 21 2022
From Amiram Eldar, Jul 24 2024: (Start)
a(n) = A008472(n) - A063956(n).
Additive with a(p^e) = p if e >= 2, and 0 otherwise. (End)
MAPLE
a:= proc(n) option remember; add(`if`(i[2]>1, i[1], 0), i=ifactors(n)[2]) end:
seq(a(n), n=1..100); # Alois P. Heinz, Jun 24 2018
MATHEMATICA
Array[Total@ Select[FactorInteger@ #, Last@ # > 1 &][[All, 1]] &, 105] (* Michael De Vlieger, Dec 06 2018 *)
PROG
(PARI) { for (n=1, 1000, f=factor(n)~; a=0; for (i=1, length(f), if (f[2, i]>1, a+=f[1, i])); write("b063958.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 04 2009
CROSSREFS
Cf. A007947 (rad), A008472 (sopf).
Sequence in context: A263145 A057108 A349435 * A349434 A126164 A340317
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Sep 04 2001
STATUS
approved