A279455 - OEIS

%I #15 May 19 2017 14:32:45

%S 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,

%T 34,37,38,41,43,44,46,47,48,52,53,54,58,59,61,62,67,68,70,71,73,74,76,

%U 79,80,82,83,86,89,90,92,94,97,101,103,105,106,107,109,110,112,113,116,118

%N Numbers n such that the number of nonprime divisors of n divides n.

%C Numbers n such that A033273(n) divides n.

%C 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).

%C All primes (A000040) are included in the sequence.

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

%H G. C. Greubel, <a href="/A279455/b279455.txt">Table of n, a(n) for n = 1..5000</a>

%e 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.

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

%o (PARI) isok(n) = denominator(n/sumdiv(n, d, !isprime(d))) == 1; \\ _Michel Marcus_, Dec 17 2016

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

%K nonn,easy

%O 1,2

%A _Ilya Gutkovskiy_, Dec 12 2016