

A109425


Numbers k such that tau(k)/omega(k) is an integer, where tau(k) = number of divisors of k and omega(k) = number of distinct prime factors of k.


3



2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79
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OFFSET

1,1


COMMENTS

Integers greater than 1 and not in A109426.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


EXAMPLE

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


MAPLE

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


MATHEMATICA

f[n_] := DivisorSigma[0, n]/Length[FactorInteger[n]]; Select[ Range[2, 80], IntegerQ[ f[ # ]] &] (* Robert G. Wilson v, Jun 30 2005 *)


CROSSREFS

Complement is A109426.
Cf. A000005, A001221.
Sequence in context: A070915 A004441 A004438 * A226537 A153679 A273887
Adjacent sequences: A109422 A109423 A109424 * A109426 A109427 A109428


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Jun 28 2005


STATUS

approved



