OFFSET
1,1
COMMENTS
Positive integers k such that sigma(k) > 2*k and sigma(k) = a^b where both a and b are greater than 1.
If k is a term with sigma(k) a square, and p and q are members of A066436 that do not divide k, then k*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 *)
PROG
(PARI) is(k) = {my(s = sigma(k)); s > 2*k && ispower(s); } \\ Amiram Eldar, Aug 02 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Walter Kehowski, Dec 01 2006
STATUS
approved