A109426 Numbers n such that tau(n)/omega(n) is not an integer [tau(n) =number of divisors of n; omega(n)=number of distinct prime factors of n].

30, 36, 42, 66, 70, 78, 100, 102, 105, 110, 114, 120, 130, 138, 144, 154, 165, 168, 170, 174, 182, 186, 190, 195, 196, 222, 225, 230, 231, 238, 240, 246, 255, 258, 264, 266, 270, 273, 280, 282, 285, 286, 290, 310, 312, 318, 322, 324, 336, 345, 354, 357, 366

Offset

1,1

Comments

Integers greater than 1 and not in A109425.

Links

Enrique Pérez Herrero, Table of n, a(n) for n = 1..10000

Example

The number 36 is 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.
The number 12 is not 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.

Maple

with(numtheory): b:=proc(n) if type(tau(n)/nops(factorset(n)), integer)=false then n else fi end: seq(b(n), n=2..400);

Mathematica

f[n_] := DivisorSigma[0, n]/Length[FactorInteger[n]]; Select[ Range[2, 369], !IntegerQ[ f[ # ]] &] (* Robert G. Wilson v, Jun 30 2005 *)
Select[Range[2, 400], !IntegerQ[DivisorSigma[0, #]/PrimeNu[#]]&] (* Harvey P. Dale, Oct 03 2015 *)

Prog

(PARI) is(n)=numdiv(n)%omega(n)>0 \\ Charles R Greathouse IV, May 15 2013

Crossrefs

Complement is A109425.

Sequence in context: A325264 A345382 A227680 * A167325 A051657 A257439

Adjacent sequences: A109423 A109424 A109425 * A109427 A109428 A109429

Keyword

nonn

Author

Emeric Deutsch, Jun 28 2005

Status

approved