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
Keywords
Examples
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.
Links
- Enrique Pérez Herrero, Table of n, a(n) for n = 1..10000
Crossrefs
Complement is A109425.
Programs
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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);
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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 *)
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PARI
is(n)=numdiv(n)%omega(n)>0 \\ Charles R Greathouse IV, May 15 2013
Comments