A074946 Positive integers n for which the sum of the prime-factorization exponents of n (bigomega(n) = A001222(n)) divides n.

2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 16, 17, 18, 19, 22, 23, 24, 26, 27, 29, 30, 31, 34, 36, 37, 38, 40, 41, 42, 43, 45, 46, 47, 53, 56, 58, 59, 60, 61, 62, 63, 66, 67, 71, 73, 74, 75, 78, 79, 80, 82, 83, 84, 86, 88, 89, 94, 96, 97, 99, 100, 101, 102, 103, 104, 105, 106

Offset: 1

Author

Benoit Cloitre, Oct 05 2002

Keywords

• easy
• nonn

Comments

If n is prime, trivially n is in the sequence.

The asymptotic density of this sequence is 0 (Erdős and Pomerance, 1990). - Amiram Eldar, Jul 10 2020

Links

• Keenan J. A. Down, Table of n, a(n) for n = 1..10000
• Paul Erdős and Carl Pomerance, On a theorem of Besicovitch: values of arithmetic functions that divide their arguments, Indian J. Math., Vol. 32 (1990), pp. 279-287.

Crossrefs

Cf. A001222, A134334 (complement).

Programs

Mathematica

Select[Range[2, 120], Divisible[#, PrimeOmega[#]] &] (* Jean-François Alcover, Jun 08 2013 *)

Formula

a(n) seems to be asymptotic to c*n*log(log(n)) with 1.128 < c < 1.13.

Extensions

Revised definition from Leroy Quet, Sep 11 2008

More terms from Keenan J. A. Down, Dec 08 2016

Smaller boundary for 'c' from Keenan J. A. Down, Dec 08 2016