

A109510


Values of n such that sigma(n)2n (the abundance of n) is a (nonnegative) square.


2



6, 12, 28, 70, 88, 108, 168, 220, 348, 496, 550, 580, 726, 748, 798, 910, 918, 952, 1032, 1120, 1200, 1240, 1504, 1644, 1672, 1840, 1888, 2140, 2205, 2392, 2470, 2472, 2814, 3190, 3222, 3580, 3804, 4030, 4648, 4732, 4758, 5032, 5670, 5830
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OFFSET

1,1


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Abundance


EXAMPLE

12 is in the sequence since sigma(12)  2*12 = 28  24 = 4 = 2^2 is a square.


MATHEMATICA

Select[Range[6000], IntegerQ@Sqrt[DivisorSigma[1, #]  2 #] &] (* Amiram Eldar, Jun 22 2019 *)


PROG

(PARI) isok(n) = issquare(sigma(n)  2*n); \\ Michel Marcus, Jun 22 2019


CROSSREFS

Cf. A000203, A000290, A023196, A033880.
Cf. A000396 (perfect numbers: a subsequence).
Sequence in context: A325812 A323652 A223346 * A034715 A294730 A079390
Adjacent sequences: A109507 A109508 A109509 * A109511 A109512 A109513


KEYWORD

nonn


AUTHOR

Eric W. Weisstein, Jun 30 2005


EXTENSIONS

Name clarified by Amiram Eldar, Jun 22 2019


STATUS

approved



