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A279455 Numbers n such that the number of nonprime divisors of n divides n. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A032846 A023777 A074946 * A050687 A098908 A097296

Adjacent sequences:  A279452 A279453 A279454 * A279456 A279457 A279458

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Dec 12 2016

STATUS

approved

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Last modified May 19 22:32 EDT 2019. Contains 323411 sequences. (Running on oeis4.)