A109421 Numbers n such that tau(n)/bigomega(n) is an integer [tau(n)=number of divisors of n; bigomega(n)=number of prime divisors of n, counted with multiplicities].

2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 28, 29, 31, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89

Offset

1,1

Comments

Integers greater than 1 and not in A109422.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

12 is in the sequence because tau(12)=6 (1,2,3,4,6,12) and bigomega(12)=3 (2,2,3) and so tau(12)/bigomega(12)=2.
16 is not in the sequence because tau(16)=5 (1,2,4,8,16) and bigomega(16)=4 (2,2,2,2) and so tau(16)/bigomega(16)=5/4.

Maple

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

Mathematica

f[n_] := DivisorSigma[0, n]/Plus @@ Last /@ FactorInteger[n]; Select[ Range[2, 89], IntegerQ[ f[ # ]] &] (* Robert G. Wilson v, Jun 29 2005 *)
Select[Range[2, 100], IntegerQ[DivisorSigma[0, #]/PrimeOmega[#]]&] (* Harvey P. Dale, Aug 14 2019 *)

Prog

(PARI) is(n)=my(f=factor(n)); n>1 && numdiv(f)%vecsum(f[, 2])==0 \\ Charles R Greathouse IV, Apr 27 2015

Crossrefs

Cf. A109422.

Sequence in context: A007916 A052485 A341646 * A335433 A345172 A212167

Adjacent sequences: A109418 A109419 A109420 * A109422 A109423 A109424

Keyword

nonn

Author

Emeric Deutsch, Jun 28 2005

Status

approved