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A293234
a(n) is the number of proper divisors of n that are square.
5
0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 2, 3, 1, 1, 1, 2, 1
OFFSET
1,8
COMMENTS
First occurrence of k: 2, 8, 32, 72, 144, 288, 576, 1152, 2304, 4608, 3600, 7200, 36864, 20736, 14400, 28800, 32400, 64800, 57600, 115200, 663552, 18874368, 129600, 259200, 3359232, 810000, 921600, 1843200, 518400, 1036800, 705600, 1411200, etc. - Robert G. Wilson v, Oct 08 2017
FORMULA
a(n) = Sum_{d|n, d<n} A010052(d).
a(n) = A046951(n) - A010052(n).
G.f.: Sum_{k>=1} x^(2*k^2) / (1 - x^(k^2)). - Ilya Gutkovskiy, Apr 13 2021
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Pi^2/6 (A013661). - Amiram Eldar, Dec 01 2023
MATHEMATICA
f[n_] := Length@ Select[ Sqrt@ Most@ Divisors@ n, IntegerQ]; Array[f, 105] (* Robert G. Wilson v, Oct 08 2017 *)
PROG
(PARI) A293234(n) = sumdiv(n, d, (d<n)*ispower(d, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 08 2017
STATUS
approved