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A079584
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Number of ones in the binary expansion of n!.
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9
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1, 1, 1, 2, 2, 4, 4, 6, 6, 6, 11, 7, 12, 12, 12, 18, 18, 22, 23, 17, 22, 25, 28, 31, 29, 30, 35, 38, 42, 40, 48, 42, 42, 46, 51, 56, 51, 58, 59, 64, 63, 66, 64, 71, 74, 70, 77, 81, 89, 87, 89, 90, 88, 94, 87, 99, 103, 98, 101, 109, 113, 103, 113, 120, 120, 109, 123, 121, 130, 121
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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a(5) = 4 because 5! = 120 and 120_10 = 1111000_2, with 4 ones.
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MAPLE
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seq(convert(convert(n!, base, 2), `+`), n=0..1000); # Robert Israel, Sep 18 2014
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MATHEMATICA
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Table[DigitCount[n!, 2, 1], {n, 70}] (* Harvey P. Dale, Jul 10 2012 *)
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PROG
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(PARI) for(n=1, 300, b=binary(n!); print1(sum(k=1, length(b), b[k])", "))
(Python)
import math
def a(n):
return bin(math.factorial(n))[2:].count("1") # Indranil Ghosh, Dec 23 2016
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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Jose R. Brox (tautocrona(AT)terra.es), Jan 26 2003
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EXTENSIONS
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STATUS
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approved
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