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

1,1

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.

Formula

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

Mathematica

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

Crossrefs

Cf. A001222, A134334 (complement).

Sequence in context: A032846 A023777 A329298 * A279455 A050687 A098908

Adjacent sequences: A074943 A074944 A074945 * A074947 A074948 A074949

Keyword

easy,nonn

Author

Benoit Cloitre, Oct 05 2002

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

Status

approved