A137944 Numbers such that the number of composite divisors is a multiple of the number of prime divisors.

2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 36, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 100, 101, 103, 107, 109, 113, 120, 121, 125, 127, 128, 131, 137, 139, 144, 149, 151, 157, 163, 167, 168, 169, 173, 179, 181, 191, 193

Offset: 1

Author

Reinhard Zumkeller, Feb 24 2008

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Divisor Function.

Crossrefs

Cf. A001221, A055212.

Disjoint union of A000961 and A137945.

Programs

Mathematica

aQ[n_] := Divisible[DivisorSigma[0, n] - 1,  PrimeNu[n]]; Select[Range[2, 193], aQ] (* Amiram Eldar, Aug 31 2019 *)

PARI

isok(k) = if(k == 1, 0, my(f = factor(k)); !((numdiv(f)-1) % omega(f))); \\ Amiram Eldar, Apr 18 2025

Formula

A055212(a(n)) mod A001221(a(n)) = 0.