A109427 Numbers n such that sigma(n)/omega(n) is an integer [sigma(n) =sum of divisors of n; omega(n)=number of distinct prime factors of n].

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77

Offset

1,1

Comments

Integers greater than 1 and not in A109428.

What is the density of this sequence? - Charles R Greathouse IV, Sep 01 2015

Links

Enrique Pérez Herrero, 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 omega(12)=2 (2,3) and so sigma(12)/omega(12)=14.
The number 36 is not 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.

Maple

with(numtheory): a:=proc(n) if type(sigma(n)/nops(factorset(n)), integer)=true then n else fi end: seq(a(n), n=2..90);

Mathematica

Select[Range[2, 80], IntegerQ[DivisorSigma[1, #]/PrimeNu[#]]&] (* Harvey P. Dale, Aug 13 2021 *)

Prog

(PARI) is(n)=if(n<2, return(0)); my(f=factor(n)); sigma(f)%omega(f)==0 \\ Charles R Greathouse IV, Sep 01 2015

Crossrefs

Cf. A109428.

Sequence in context: A317257 A242031 A335376 * A325360 A325400 A342523

Adjacent sequences: A109424 A109425 A109426 * A109428 A109429 A109430

Keyword

nonn

Author

Emeric Deutsch, Jun 28 2005

Status

approved