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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].
2
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 PĂ©rez 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
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jun 28 2005
STATUS
approved