OFFSET
1,3
COMMENTS
This sequence is infinite since it contains all the numbers of the form 4^(k^2). - Giovanni Resta, May 28 2016
EXAMPLE
0' = 0 = 0^2; 1' = 0 = 0^2; 4' = 4 = 2^2; 256' = 1024 = 32^2; 11664' = 46656 = 216^2.
MAPLE
with(numtheory): P:=proc(q) local a, n, p;
for n from 0 to q do a:=n^2*add(op(2, p)/op(1, p), p=ifactors(n^2)[2]);
if trunc(sqrt(a))*trunc(sqrt(a))=a then print(n^2); fi;
od; end: P(10^9);
MATHEMATICA
{0, 1}~Join~Select[Range[2, 10^5]^2, IntegerQ@ Sqrt[# Total[#2/#1 & @@@ FactorInteger[#]]] &] (* Michael De Vlieger, Oct 19 2021 *)
PROG
(PARI) ad(n) = if (n<1, 0, my(f = factor(n)); n*sum(k=1, #f~, f[k, 2]/f[k, 1]));
lista(nn) = {for (n=0, nn, if (issquare(ad(n^2)), print1(n^2, ", ")); ); } \\ Michel Marcus, Apr 08 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Apr 08 2016
EXTENSIONS
a(17)-a(23) from Giovanni Resta, May 28 2016
STATUS
approved