A109423 Numbers n such that sigma(n)/bigomega(n) is an integer [sigma(n) = sum of divisors of n; bigomega(n) = number of prime divisors of n, counted with multiplicity].

2, 3, 5, 6, 7, 8, 10, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92

Offset

1,1

Comments

Integers greater than 1 and not in A109424.

Contains all primes and squarefree semiprimes (A006881). - Robert Israel, Jan 16 2017

Links

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

Example

The number 24 is 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.
The number 12 is not 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.

Maple

with(numtheory): a:=proc(n) if type(sigma(n)/bigomega(n), integer)=true then n else fi end: seq(a(n), n=2..110);

Mathematica

PrimeOmega[n_] := Plus @@ FactorInteger[n][[All, 2]]; Select[Range[2, 100], IntegerQ[DivisorSigma[1, #]/PrimeOmega[#]] &] (* Jean-François Alcover, May 02 2013 *)

Prog

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

Crossrefs

Cf. A006881, A109424.

Sequence in context: A285420 A028737 A371731 * A028801 A348751 A348738

Adjacent sequences: A109420 A109421 A109422 * A109424 A109425 A109426

Keyword

nonn

Author

Emeric Deutsch, Jun 28 2005

Status

approved