OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
EXAMPLE
a(2)=75 because sum of aliquot divisors of 75 = 1 + 3 + 5 + 15 + 25 = 49 = 7^2 and product of aliquot divisors of 75 = 1*3*5*15*25 = 75^2.
MATHEMATICA
Do[d = Delete[ Divisors[n], -1]; If[ !PrimeQ[n] && IntegerQ[ Sqrt[ Apply[ Plus, d]]] && IntegerQ[ Sqrt[ Apply[ Times, d]]], Print[n]], {n, 2, 10^4} ]
spsQ[n_]:=Module[{d=Most[Divisors[n]]}, CompositeQ[n]&&AllTrue[{Sqrt[ Total[ d]], Sqrt[Times@@d]}, IntegerQ]]; Select[Range[5100], spsQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 14 2018 *)
PROG
(PARI) pad(n)= { local(d, p=1); d=divisors(n); for (i=1, length(d) - 1, p*=d[i]); return(p) }
{ n=0; for (m=2, 10^9, s=sigma(m) - m; if (s>1 && issquare(s) && issquare(pad(m)), write("b064116.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 07 2009
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Shyam Sunder Gupta, Sep 09 2001
EXTENSIONS
More terms from Robert G. Wilson v, Oct 05 2001
STATUS
approved