A073803 Numbers k such that the number of divisors of k is smaller than that of sigma(k).

3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89, 91

Offset: 1

Author

Labos Elemer, Aug 13 2002

Keywords

• nonn

Examples

			k = 96: divisors(96) = {1,2,3,4,6,8,12,16,24,32,48,96}, 12 divisors; divisors(sigma(96)) = {1,2,3,4,6,7,9,12,14,18,21,28,36,42,63,84,126,252}, 18 divisors; 12 < 18, so 96 is a term.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000203, A062068, A073802, A073804, A037197.

Programs

Maple

filter:= proc(n) uses numtheory; tau(n) < tau(sigma(n)) end proc:
select(filter, [$1..100]); # Robert Israel, Aug 03 2020

Mathematica

Do[s=DivisorSigma[0, DivisorSigma[1, n]]; s0=DivisorSigma[0, n]; If[Greater[s0, s], Print[n]], {n, 1, 1000}]
Select[Range[100],DivisorSigma[0,#]Harvey P. Dale, Sep 22 2019 *)

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)).