A064499 Composite numbers n such that product of aliquot divisors of n is a perfect square.

12, 16, 18, 20, 28, 32, 44, 45, 48, 50, 52, 63, 68, 75, 76, 80, 81, 92, 98, 99, 112, 116, 117, 124, 147, 148, 153, 162, 164, 171, 172, 175, 176, 180, 188, 192, 207, 208, 212, 236, 242, 243, 244, 245, 252, 256, 261, 268, 272, 275, 279, 284, 288, 292, 300, 304

Offset: 1

Author

Robert G. Wilson v, Oct 05 2001

Keywords

• base
• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Crossrefs

Cf. A048699, A007956.

Programs

Mathematica

Do[ If[ !PrimeQ[n] && IntegerQ[ Sqrt[ Apply[ Times, Delete[ Divisors[n], -1]]]], Print[n]], {n, 2, 500} ]

PARI

pad(n)=my(d=divisors(n), p=1); for (i=1, #d-1, p*=d[i]); p
n=0; for (m=2, 10^9, if (!isprime(m) && issquare(pad(m)), write("b064499.txt", n++, " ", m); if (n==1000, break))) \\ Harry J. Smith, Sep 16 2009

PARI

is(n)=!isprime(n) && (ispower(n,4) || numdiv(n)%4==2) && n>1 \\ Charles R Greathouse IV, Oct 17 2015