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A079584 Number of ones in the binary expansion of n!. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Florian Luca, The number of non-zero digits of n!, Canad. Math. Bull. 45 (2002), pp. 115-118.

Carlo Sanna, On the sum of digits of the factorial, arXiv:1409.4912 [math.NT], 2014.

Carlo Sanna, On the sum of digits of the factorial, Journal of Number Theory 147 (2015), pp. 836-841.

FORMULA

a(n) << n log n. - Charles R Greathouse IV, Mar 27 2013

a(n) = A000120(A000142(n)). - Michel Marcus, Sep 18 2014

EXAMPLE

a(5) = 4 because 5! = 120 and 120_10 = 1111000_2, with 4 ones.

MAPLE

seq(convert(convert(n!, base, 2), `+`), n=1..1000); # Robert Israel, Sep 18 2014

MATHEMATICA

Table[DigitCount[n!, 2, 1], {n, 70}] (* Harvey P. Dale, Jul 10 2012 *)

PROG

(PARI) for(n=1, 300, b=binary(n!); print1(sum(k=1, length(b), b[k])", "))

(PARI) a(n)=hammingweight(n!) \\ Charles R Greathouse IV, Mar 27 2013

(Python)

import math

def a(n):

    return bin(math.factorial(n))[2:].count("1") # Indranil Ghosh, Dec 23 2016

CROSSREFS

Cf. A000120 (binary weight), A000142 (factorial), A004152 (sum of decimal digits).

Sequence in context: A070320 A124195 A220662 * A179291 A004079 A096494

Adjacent sequences:  A079581 A079582 A079583 * A079585 A079586 A079587

KEYWORD

nonn

AUTHOR

Jose R. Brox (tautocrona(AT)terra.es), Jan 26 2003

STATUS

approved

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Last modified November 23 16:18 EST 2020. Contains 338590 sequences. (Running on oeis4.)