A074632 Numbers k such that the sum of 2nd, 3rd, 4th and 5th powers of divisors of k are divisible by sum of divisors of k.

1, 20, 64, 500, 729, 1024, 1280, 4096, 4352, 14580, 15625, 32000, 39168, 46656, 47360, 59049, 65536, 117649, 144640, 161024, 262144, 312500, 364500, 509184, 531441, 746496, 796797, 933120, 1000000, 1180980, 1184000, 1449216, 1771561

Offset: 1

Author

Labos Elemer, Aug 27 2002

Keywords

• nonn

Examples

			For k = 20: sigma(k) = 42 ,sigma_2(k) = 546 = 13 * 42, sigma_3(k) = 9198 = 219 * 42, sigma_4(k) = 170898 = 4069 * 42, sigma_5(k) = 3304182 = 78671 * 42.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..269 (terms up to 10^10)

Crossrefs

See also A020487, A046841, A046870, A046871.

Cf. A000203, A001157, A001158, A001159, A001160.

Programs

Mathematica

Select[Range[2000000],And@@Divisible[DivisorSigma[Range[2,5],#], DivisorSigma[ 1,#]]&] (* Harvey P. Dale, Jan 01 2012 *)

PARI

is(k) = {my(f = factor(k), s = sigma(f)); for(k = 2, 5, if(sigma(f, k) % s, return(0))); 1; }  \\ Amiram Eldar, Jun 15 2024