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

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Divisor Function.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001221, A055212.

Disjoint union of A000961 and A137945.

Sequence in context: A326534 A046686 A383099 * A359390 A323306 A325247

Adjacent sequences: A137941 A137942 A137943 * A137945 A137946 A137947

Keyword

nonn

Author

Reinhard Zumkeller, Feb 24 2008

Status

approved