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A090616
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Exponent of highest power of 4 dividing n!.
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10
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0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 7, 7, 8, 8, 9, 9, 9, 9, 11, 11, 11, 11, 12, 12, 13, 13, 15, 15, 16, 16, 17, 17, 17, 17, 19, 19, 19, 19, 20, 20, 21, 21, 23, 23, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 28, 28, 31, 31, 32, 32, 33, 33, 33, 33, 35, 35, 35, 35, 36
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,7
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LINKS
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FORMULA
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a(n) = A090622(n, 4) = floor(A011371(n)/2) = floor((floor(n/2) + floor(n/4) + floor(n/8) + floor(n/16) + ...)/2).
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EXAMPLE
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a(6)=2 since 6! = 720 = 4^2 * 45.
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MATHEMATICA
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PROG
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(PARI) a(n) = valuation( n!, 4 ); /* Joerg Arndt, Mar 10 2013 */
(Python 3.10+)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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