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%I #18 Jun 14 2021 16:12:42
%S 0,2,3,4,5,11,7,12,9,17,11,25,13,23,23,24,17,35,19,39,31,35,23,57,25,
%T 41,36,53,29,71,31,56,47,53,47,79,37,59,55,87,41,95,43,81,74,71,47,
%U 117,49,87,71,95,53,116,71,117,79,89,59,165,61,95,100,112,83,143,67,123,95,143,71,183,73,113,118,137,95,167,79,179,108,125,83
%N Sum of the divisors of n whose square does not divide n.
%F a(n) = Sum_{k=1..n} k * (ceiling(n/k^2) - floor(n/k^2)) * (1 - ceiling(n/k) + floor(n/k)).
%F a(n) = A000203(n) - A069290(n). - _Rémy Sigrist_, Jun 14 2021
%e a(16) = 24; The divisors of 16 whose square does not divide 16 are 8 and 16. The sum of the divisors is then 8 + 16 = 24.
%t Table[Sum[k (Ceiling[n/k^2] - Floor[n/k^2]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]
%o (PARI) a(n) = sumdiv(n, d, if (n % d^2, d)); \\ _Michel Marcus_, Jun 13 2021
%o (Python 3.8+)
%o from math import prod
%o from sympy import factorint
%o def A345320(n):
%o f = factorint(n).items()
%o return (prod(p**(q+1)-1 for p, q in f) - prod(p**(q//2+1)-1 for p, q in f))//prod(p-1 for p, q in f) # _Chai Wah Wu_, Jun 14 2021
%Y Cf. A000203, A056595, A069290.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, Jun 13 2021
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