A073804 Numbers k such that the number of divisors of k is greater than that of sigma(k).

4, 9, 16, 18, 25, 36, 48, 50, 64, 72, 80, 81, 100, 112, 144, 162, 180, 192, 196, 200, 208, 225, 240, 252, 256, 288, 289, 300, 320, 324, 336, 400, 432, 441, 448, 450, 468, 484, 512, 576, 578, 592, 624, 625, 648, 676, 700, 704, 720, 729, 768, 784, 800, 810, 832

Offset: 1

Author

Labos Elemer, Aug 13 2002

Keywords

• nonn

Examples

			k = 25: divisors(25) = {1,5,25}, 3 divisors; divisors(sigma(25)) = {1,31}, 2 divisors; 2 < 3, so 25 is a term.
k = 48: divisors(48) = {1,2,3,4,6,8,12,16,24,48}, 10 divisors; divisors(sigma(48)) = {1,2,4,31,62,124}, 6 divisors, 6 < 10 so 48 is a term.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A000005, A000203, A062068, A073802, A073803, A037197.

Programs

Mathematica

Do[s=DivisorSigma[0, DivisorSigma[1, n]]; s0=DivisorSigma[0, n]; If[Greater[s0, s], Print[n]], {n, 1, 1000}]
Select[Range[900],DivisorSigma[0,#]>DivisorSigma[0,DivisorSigma[1,#]]&] (* Harvey P. Dale, Jan 18 2017 *)

PARI

isok(k) = {my(f = factor(k)); numdiv(f) > numdiv(sigma(f));} \\ Amiram Eldar, Mar 07 2025

Formula

Solutions to A000005(x) > A062068(x) = A000005(A000203(x)).