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A293235 a(n) is the sum of proper divisors of n that are square. 3
0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 10, 1, 5, 1, 1, 1, 5, 1, 1, 10, 5, 1, 1, 1, 21, 1, 1, 1, 14, 1, 1, 1, 5, 1, 1, 1, 5, 10, 1, 1, 21, 1, 26, 1, 5, 1, 10, 1, 5, 1, 1, 1, 5, 1, 1, 10, 21, 1, 1, 1, 5, 1, 1, 1, 50, 1, 1, 26, 5, 1, 1, 1, 21, 10, 1, 1, 5, 1, 1, 1, 5, 1, 10, 1, 5, 1, 1, 1, 21, 1, 50, 10, 30, 1, 1, 1, 5, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

a(n) = 1 if and only if n > 1 is squarefree or the square of a prime. - Robert Israel, Oct 08 2017

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

a(n) = Sum_{d|n, d<n} A010052(d)*d.

a(n) = A035316(n) - (A010052(n)*n).

MAPLE

A035316:= n -> mul((p[1]^(p[2]+2-(p[2] mod 2))-1)/(p[1]^2-1), p = ifactors(n)[2]):

f:= n -> A035316(n) - `if`(issqr(n), n, 0):

map(f, [$1..100]); # Robert Israel, Oct 08 2017

PROG

(PARI) A293235(n) = sumdiv(n, d, (d<n)*ispower(d, 2)*d);

CROSSREFS

Cf. A010052, A035316, A293228, A293234.

Sequence in context: A304042 A109768 A069293 * A066803 A089608 A250131

Adjacent sequences:  A293232 A293233 A293234 * A293236 A293237 A293238

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 08 2017

STATUS

approved

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Last modified June 17 19:10 EDT 2019. Contains 324198 sequences. (Running on oeis4.)