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Search: id:A109425
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| A109425 |
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Numbers n such that tau(n)/omega(n) is an integer [tau(n) =number of divisors of n; omega(n)=number of distinct prime factors of n]. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Integers greater than 1 and not in A109426.
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EXAMPLE
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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.
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MAPLE
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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);
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MATHEMATICA
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f[n_] := DivisorSigma[0, n]/Length[FactorInteger[n]]; Select[ Range[2, 80], IntegerQ[ f[ # ]] &] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 30 2005)
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CROSSREFS
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Complement is A109426.
Sequence in context: A070915 A004441 A004438 this_sequence A087143 A080683 A124231
Adjacent sequences: A109422 A109423 A109424 this_sequence A109426 A109427 A109428
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 28 2005
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