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

1,1

Links

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

Formula

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

Example

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.

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, #]<DivisorSigma[0, DivisorSigma[1, #]]&] (* Harvey P. Dale, Sep 22 2019 *)

Prog

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

Crossrefs

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

Sequence in context: A136806 A253550 A295307 * A378501 A336353 A182851

Adjacent sequences: A073800 A073801 A073802 * A073804 A073805 A073806

Keyword

nonn

Author

Labos Elemer, Aug 13 2002

Status

approved