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Search: id:A133924
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| A133924 |
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a(n) = number of exponents occurring only once each in the prime-factorization of n!. |
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+0
1
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| 0, 0, 1, 0, 2, 1, 3, 2, 2, 2, 4, 3, 3, 3, 2, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 6, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9
(list; graph; listen)
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OFFSET
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0,5
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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14! is factored into primes as 2^11 * 3^5 * 5^2 * 7^2 * 11^1 * 13^1. The exponent 1 and 2 each occur more than once. So the exponents occurring only once each are 5 and 11. Therefore a(14) = 2.
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MAPLE
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A133924 := proc(n) local ifs, a, i ; if n <= 1 then RETURN(0) ; else ifs := ifactors(n!)[2] ; ifs := sort([seq(op(2, i), i=ifs)]) ; a :=0 ; for i from 1 to nops(ifs) do if i = 1 or op(i, ifs) <> op(i-1, ifs) then if i=nops(ifs) or op(i, ifs) <> op(i+1, ifs) then a := a+1 ; fi ; fi ; od: RETURN(a) ; fi ; end: seq(A133924(n), n=0..120) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 30 2008
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CROSSREFS
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Cf. A071626.
Sequence in context: A103151 A035221 A035191 this_sequence A023135 A066272 A058773
Adjacent sequences: A133921 A133922 A133923 this_sequence A133925 A133926 A133927
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Jan 07 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 30 2008
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