

A263928


Integers m such that sigma(m)^2 is divisible by m.


4



1, 6, 24, 28, 120, 224, 234, 270, 496, 588, 600, 672, 864, 1080, 1521, 1638, 1782, 2016, 3724, 4320, 4680, 5733, 6048, 6200, 6552, 7128, 8128, 11172, 11466, 15872, 17280, 18144, 18600, 18620, 21600, 22932, 26208, 26460, 27000, 30240, 32640, 32760, 33516, 35640
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OFFSET

1,2


COMMENTS

Previous name was: "Numbers such that the product of the sum of their divisors and the sum of the reciprocals of their divisors is an integer".
The multiplyperfect numbers (A007691) are a subset of this sequence.
This is a subsequence of A175200.  Michel Marcus, Nov 03 2015
Alternative definition: Numbers m such that Sum_{i = 1..k} (sigma(m)  d_i) / d_i is an integer, where d_i are the k divisors of m.  Paolo P. Lava, Mar 23 2017


LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..100


EXAMPLE

Divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Their sum is sigma(24) = 60 while the sum of their reciprocals is 1/1 + 1/2 + 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24 = 5/2. Finally 60 * 5/2 = 150.


MAPLE

with(numtheory): P:=proc(q) local n;
for n from 1 to q do if type(sigma(n)^2/n, integer) then print(n);
fi; od; end: P(10^6);


PROG

(PARI) isok(n) = (sigma(n)^2 % n) == 0; \\ Michel Marcus, Nov 03 2015


CROSSREFS

Cf. A000203, A007691, A017665, A017666, A175200, A263983.
Sequence in context: A175200 A293453 A118372 * A219362 A226476 A216793
Adjacent sequences: A263925 A263926 A263927 * A263929 A263930 A263931


KEYWORD

nonn


AUTHOR

Paolo P. Lava, Oct 30 2015


EXTENSIONS

New name from Michel Marcus, Nov 03 2015


STATUS

approved



