A109424 Numbers n such that sigma(n)/bigomega(n) is not an integer [sigma(n) = sum of divisors of n; bigomega(n) = number of prime divisors of n, counted with multiplicity].

4, 9, 12, 16, 25, 27, 28, 32, 36, 40, 48, 49, 52, 63, 64, 75, 76, 80, 81, 90, 100, 104, 112, 117, 121, 124, 128, 136, 144, 148, 162, 169, 171, 172, 175, 176, 180, 192, 196, 208, 225, 232, 234, 243, 244, 252, 256, 268, 272, 273, 279, 289, 292, 296, 300, 306, 316

Offset

1,1

Comments

Integers greater than 1 and not in A109423.

Includes all squares > 1. - Robert Israel, Jan 16 2017

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The number 12 is in the sequence because sigma(12)=28 (1+2+3+4+6+12) and bigomega(12)=3 (2,2,3) and so sigma(12)/bigomega(12) = 28/3.
The number 24 is not in the sequence because sigma(24)=60 (1+2+3+4+6+8+12+24) and bigomega(24)=4 (2,2,2,3) and so sigma(24)/bigomega(24) = 15.

Maple

with(numtheory): b:=proc(n) if type(sigma(n)/bigomega(n), integer)=false then n else fi end: seq(b(n), n=2..340);

Mathematica

PrimeOmega[n_] := Plus @@ FactorInteger[n][[All, 2]]; Select[Range[2, 320], ! IntegerQ[DivisorSigma[1, #]/PrimeOmega[#]] &] (* Jean-François Alcover, May 02 2013 *)
Select[Range[2, 320], !IntegerQ[DivisorSigma[1, #]/PrimeOmega[#]]&] (* Harvey P. Dale, Aug 12 2020 *)

Prog

(PARI) isok(n) = denominator(sigma(n)/bigomega(n)) != 1; \\ Michel Marcus, Jan 17 2017

Crossrefs

Cf. A000290, A109423.

Sequence in context: A225870 A171920 A141037 * A034019 A034018 A320924

Adjacent sequences: A109421 A109422 A109423 * A109425 A109426 A109427

Keyword

nonn

Author

Emeric Deutsch, Jun 28 2005

Status

approved