A054027 Numbers that do not divide their sum of divisors.

2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset: 1

Author

Asher Auel, Jan 19 2000

Keywords

• nonn

Comments

Does not contain numbers like 1, 120, 672, 30240, 32760, 523776,.. which are in A132999. - R. J. Mathar, Jun 13 2025

Crossrefs

Complement of A007691. Cf. A000203, A054024.

Programs

Maple

with(numtheory): [seq(`if`(sigma(i) mod i <> 0,i,print( )),i=1..90)];

Mathematica

Select[Range[100],!Divisible[DivisorSigma[1,#],#]&] (* Harvey P. Dale, May 29 2019 *)

PARI

isok(m) = (sigma(m) % m) != 0; \\ Michel Marcus, Jun 20 2021