A124142 Abundant numbers n such that sigma(n) is a perfect power.

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

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;

Mathematica

filterQ[n_] := With[{s = DivisorSigma[1, n]}, s > 2n && GCD @@ FactorInteger[s][[All, 2]] > 1];
Select[Range[4000], filterQ] (* Jean-François Alcover, Sep 16 2020 *)

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