A134608 Composite numbers such that the cube root of the sum of cubes of their prime factors is an integer.

256, 588, 693, 3840, 6561, 14157, 17787, 141960, 178360, 313600, 337365, 350000, 387072, 390625, 407442, 432000, 466560, 531674, 535815, 541310, 664909, 697851, 1044582, 1262056, 1264640, 1299272, 1374327, 1547570, 1608575, 1660360

Offset: 1

Author

Hieronymus Fischer, Nov 11 2007

Keywords

• nonn

Examples

			a(3)=693, since 693=3*3*7*11 and (2*3^3+7^3+11^3)^(1/3)=1728^(1/3)=12.
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A001597, A025475, A134333, A134344, A134376.

Cf. A134600, A134602, A134605, A134611, A134616, A134618, A134620.

Programs

Mathematica

criQ[n_]:=IntegerQ[Surd[Total[Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[ n]]^3],3]]; Select[Range[1670000],CompositeQ[#] && criQ[#]&] (* Harvey P. Dale, Sep 19 2021 *)

PARI

lista(m) = {for (i=2, m, if (! isprime(i), f = factor(i); s = sum (j=1, length(f~), f[j,1]^3*f[j,2]); if (ispower(s, 3), print1(i, ", "));););} \\ Michel Marcus, Apr 14 2013

Extensions

Minor edits by Hieronymus Fischer, Apr 20 2013