

A074946


Positive integers n for which the sum of the primefactorization exponents of n (bigomega(n) = A001222(n)) divides n.


19



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
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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. 279287.


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[#]] &] (* JeanFrançois 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



