

A124142


Abundant numbers n such that sigma(n) is a perfect power.


1



66, 70, 102, 210, 282, 364, 400, 510, 642, 690, 714, 770, 820, 930, 966, 1080, 1092, 1146, 1164, 1200, 1416, 1566, 1624, 1672, 1782, 2130, 2226, 2250, 2346, 2460, 2530, 2586, 2652, 2860, 2910, 2912, 3012, 3198, 3210, 3340, 3498, 3522, 3560, 3710, 3810
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OFFSET

1,1


COMMENTS

Positive integers n such that sigma(n)>2*n and sigma(n)=a^b where both a and b are greater than 1.
If n is a term with sigma(n) a square, and p and q are members of A066436 that do not divide n, then n*p*q is in the sequence. Thus if A066436 is infinite, so is this sequence.  Robert Israel, Oct 29 2018


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


EXAMPLE

a(1)=66 since sigma(66)=144=12^2.


MAPLE

with(numtheory); egcd := proc(n::posint) local L; if n>1 then L:=ifactors(n)[2]; L:=map(z>z[2], L); return igcd(op(L)) else return 1 fi; end; L:=[]: for w to 1 do for n from 1 to 10000 do s:=sigma(n); if s>2*n and egcd(s)>1 then print(n, s, ifactor(s)); L:=[op(L), n]; fi od od;


CROSSREFS

Cf. A001597, A005101, A065496, A066436.
Sequence in context: A031960 A181464 A250739 * A036207 A039538 A095751
Adjacent sequences: A124139 A124140 A124141 * A124143 A124144 A124145


KEYWORD

nonn


AUTHOR

Walter Kehowski, Dec 01 2006


STATUS

approved



