A109428 Numbers n such that sigma(n)/omega(n) is not an integer [sigma(n) =sum of divisors of n; omega(n)=number of distinct prime factors of n].

18, 36, 50, 72, 84, 98, 100, 144, 156, 162, 196, 200, 225, 228, 242, 252, 273, 288, 300, 324, 336, 338, 364, 372, 392, 399, 400, 441, 444, 468, 484, 516, 525, 532, 576, 578, 624, 648, 651, 676, 684, 700, 722, 732, 741, 756, 777, 784, 800, 804, 819, 868, 876

Offset: 1

Author

Emeric Deutsch, Jun 28 2005

Keywords

• nonn

Comments

Integers greater than 1 and not in A109427.

Examples

			The number 36 is in the sequence because sigma(36)=91 (1+2+3+4+6+9+12+18+36) and omega(36)=2 (2,3) and so sigma(36)/omega(36)=91/2.
The number 12 is not in the sequence because sigma(12)=28 (1+2+3+4+6+12) and omega(12)=2 (2,3) and so sigma(12)/omega(12)=14.
		

Links

• Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A109427.

Programs

Maple

with(numtheory): b:=proc(n) if type(sigma(n)/nops(factorset(n)),integer)=false then n else fi end: seq(b(n),n=2..1000);

Mathematica

Select[Range[2,1000],!IntegerQ[DivisorSigma[1,#]/PrimeNu[#]]&] (* Harvey P. Dale, Aug 09 2012 *)