A054010 Numbers n with property that n is divisible by the number of its proper divisors.

2, 3, 4, 5, 6, 7, 11, 13, 15, 16, 17, 19, 20, 21, 23, 27, 29, 31, 33, 37, 39, 41, 42, 43, 45, 47, 50, 51, 53, 56, 57, 59, 61, 67, 69, 70, 71, 73, 75, 79, 83, 87, 89, 93, 97, 101, 103, 105, 107, 109, 111, 113, 120, 123, 127, 129, 131, 132, 137, 139, 141, 149, 151, 154

Offset: 1

Author

Asher Auel, Jan 12 2000

Keywords

• nonn

Comments

All primes are in this sequence, having only one proper divisor. The specifically nonprime members of this sequence are in A055719. - Carl R. White, Jul 11 2012

Examples

			There are three proper divisors of 6, {1, 2, 3}, 6 is divisible by 3.
		

Links

• Carl R. White, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A032741, A033950, A054009, A055719.

Programs

Maple

[seq(`if`(i mod (tau(i)-1) = 0,i,print( )), i=2..190)];

Mathematica

Select[Range[2, 100], IntegerQ[ #/(-1+DivisorSigma[0, # ])]&] (* Wouter Meeussen, Jun 07 2005 *)

Formula

Numbers n such that A054009(n) = 0.