A075592 -id:A075592 - cp's OEIS frontend

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

Ilya Gutkovskiy, Dec 12 2016

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.

			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.

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

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

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

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

A336063 Numbers divisible by the minimal exponent in their prime factorization (A051904).

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset: 1

Amiram Eldar, Jul 07 2020

nonn

The asymptotic density of this sequence is 1 (Schinzel and Šalát, 1994).

			4 = 2^2 is a term since A051904(4) = 2 is a divisor of 4.

József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, chapter 3, p. 331.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Andrzej Schinzel and Tibor Šalát, Remarks on maximum and minimum exponents in factoring, Mathematica Slovaca, Vol. 44, No. 5 (1994), pp. 505-514.

Cf. A051904, A124184.
A005117 (except for 1) is subsequence.
Similar sequences: A033950, A005349, A006446, A074946, A075592, A007694, A112249, A336064.

h[1] = 0; h[n_] := Min[FactorInteger[n][[;; , 2]]]; Select[Range[2, 100], Divisible[#, h[#]] &]
Select[Range[2,100],Divisible[#,Min[FactorInteger[#][[All,2]]]]&] (* Harvey P. Dale, Aug 31 2020 *)

isok(m) = if (m>1, (m % vecmin(factor(m)[,2])) == 0); \\ Michel Marcus, Jul 08 2020

cp's OEIS Frontend

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

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