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

1,2

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.

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A023777 A329298 A074946 * A050687 A098908 A097296

Adjacent sequences: A279452 A279453 A279454 * A279456 A279457 A279458

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Dec 12 2016

Status

approved