A109425 -id:A109425 - cp's OEIS frontend

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

Emeric Deutsch, Jun 28 2005

nonn

Integers greater than 1 and not in A109425.

			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.

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

Complement is A109425.

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);

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 *)

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

A175785 Numbers n such that the number of distinct prime divisors of n does not divide phi(n).

Original entry on oeis.org

30, 60, 66, 102, 110, 120, 132, 138, 150, 165, 170, 174, 204, 220, 230, 240, 246, 255, 264, 276, 282, 290, 300, 318, 340, 345, 348, 354, 374, 408, 410, 426, 435, 440, 460, 470, 480, 492, 498, 506, 528, 530, 534, 550, 552, 561, 564, 580, 590, 600, 606, 615

Offset: 1

Enrique Pérez Herrero, Sep 04 2010

nonn

a(n) gives the integers where omega(n) = A001221(n) does not divide phi(n) = A000010(n).

This sequence does not contain any prime powers (A000961), nor any numbers with only two distinct prime divisors (A007774); so it is a subsequence of A000977.

			30 is in this sequence because omega(30)=3 does not divide phi(30)=8.

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

Cf. A001221, A000010, A075592, A109425, A109427, A192218, A000977, A000961, A007774.

Select[Range[2,700],Mod[EulerPhi[#],PrimeNu[#]]!=0&] (* Harvey P. Dale, Dec 29 2019 *)

isok(n) = (eulerphi(n) % omega(n) != 0) \\ Michel Marcus, Jun 12 2013

cp's OEIS Frontend

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].

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