A109425 Numbers k such that tau(k)/omega(k) is an integer, where tau(k) = number of divisors of k and omega(k) = number of distinct prime factors of k.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79

Offset

1,1

Comments

Integers greater than 1 and not in A109426.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

The number 12 is in the sequence because tau(12) = 6 (1,2,3,4,6,12) and omega(12) = 2 (2,3) and so tau(12)/omega(12) = 3.
The number 36 is not in the sequence because tau(36) = 9 (1,2,3,4,6,9,12,18,36) and omega(36) = 2 (2,3) and so tau(36)/omega(36) = 9/2.

Maple

with(numtheory): a:=proc(n) if type(tau(n)/nops(factorset(n)), integer)=true then n else fi end: seq(a(n), n=2..90);

Mathematica

f[n_] := DivisorSigma[0, n]/Length[FactorInteger[n]]; Select[ Range[2, 80], IntegerQ[ f[ # ]] &] (* Robert G. Wilson v, Jun 30 2005 *)
Select[Range[2, 80], IntegerQ[DivisorSigma[0, #]/PrimeNu[#]]&] (* Harvey P. Dale, Sep 29 2024 *)

Crossrefs

Complement is A109426.

Cf. A000005, A001221.

Sequence in context: A083243 A004441 A004438 * A357873 A226537 A349294

Adjacent sequences: A109422 A109423 A109424 * A109426 A109427 A109428

Keyword

nonn

Author

Emeric Deutsch, Jun 28 2005

Status

approved