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

1,2

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

See also A020487, A046841, A046870, A046871.

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

Sequence in context: A262486 A187156 A246877 * A225190 A228839 A331096

Adjacent sequences: A074629 A074630 A074631 * A074633 A074634 A074635

Keyword

nonn

Author

Labos Elemer, Aug 27 2002

Status

approved