A279455 Numbers n such that the number of nonprime divisors of n divides n.

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 16, 17, 19, 20, 22, 23, 24, 26, 27, 28, 29, 30, 31, 34, 37, 38, 41, 43, 44, 46, 47, 48, 52, 53, 54, 58, 59, 61, 62, 67, 68, 70, 71, 73, 74, 76, 79, 80, 82, 83, 86, 89, 90, 92, 94, 97, 101, 103, 105, 106, 107, 109, 110, 112, 113, 116, 118

Offset: 1

Author

Ilya Gutkovskiy, Dec 12 2016

Keywords

• nonn
• easy

Comments

Numbers n such that A033273(n) divides n.

Fixed points of lcm(n, tau(n)-omega(n)), where tau(n) is the number of divisors of n (A000005) and omega(n) is the number of distinct primes dividing n (A001221).

All primes (A000040) are included in the sequence.

All even semiprimes (A100484) are included in the sequence.

Examples

			12 is in the sequence because 12 has 6 divisors {1,2,3,4,6,12} out of which 4 are nonprimes {1,4,6,12} and 4 divides 12.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000005, A000040, A001221, A033950, A033273, A054010, A075592.

Programs

Mathematica

Select[Range[150], Divisible[#1, DivisorSigma[0, #1] - PrimeNu[#1]] & ]

PARI

isok(n) = denominator(n/sumdiv(n, d, !isprime(d))) == 1; \\ Michel Marcus, Dec 17 2016