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A165256
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Numbers whose number of distinct prime factors equals the number of digits in the number.
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4
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2, 3, 4, 5, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 33, 34, 35, 36, 38, 39, 40, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 62, 63, 65, 68, 69, 72, 74, 75, 76, 77, 80, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 98, 99, 102, 105, 110, 114, 120, 126, 130, 132
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Is this sequence finite? If the answer is yes, is there any estimate for the number of terms of this sequence? - Parthasarathy Nambi, Nov 16 2009
This sequence is finite since there are only finitely many primes less than 10. - Charles R Greathouse IV, Feb 04 2013
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..7812 (complete sequence)
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EXAMPLE
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The number of distinct prime factors of 4 is 1, which is the same as the number of digits in 4, so 4 is in the sequence.
The number of distinct prime factors of 21 is 2, which is the same as the number of digits in 21, so 21 is in the sequence.
However, 25 is NOT in the sequence because the number of distinct prime factors of 25 is 1, which does not match the number of digits in 25.
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MAPLE
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omega := proc(n) nops(numtheory[factorset](n)) ; end: A055642 := proc(n) max(1, ilog10(n)+1) ; end: A165256 := proc(n) option remember; local a; if n = 1 then 2; else for a from procname(n-1)+1 do if A055642(a) = omega(a) then RETURN(a) ; fi; od: fi; end: seq(A165256(n), n=1..120) ; # R. J. Mathar, Sep 17 2009
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MATHEMATICA
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Select[Range[200], IntegerLength[#] == Length[FactorInteger[#]] &] (* Harvey P. Dale, Mar 20 2011 *)
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PROG
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(PARI) is(n)=#Str(n)==omega(n) \\ Charles R Greathouse IV, Feb 04 2013
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CROSSREFS
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Sequence in context: A006644 A024898 A094210 * A175020 A050728 A230999
Adjacent sequences: A165253 A165254 A165255 * A165257 A165258 A165259
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KEYWORD
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base,nonn,fini,full
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AUTHOR
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Parthasarathy Nambi, Sep 11 2009
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EXTENSIONS
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Extended by R. J. Mathar, Sep 17 2009
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STATUS
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approved
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