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Search: id:A022559
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| A022559 |
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Sum of exponents in prime-power factorization of n!. |
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+0
13
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| 0, 0, 1, 2, 4, 5, 7, 8, 11, 13, 15, 16, 19, 20, 22, 24, 28, 29, 32, 33, 36, 38, 40, 41, 45, 47, 49, 52, 55, 56, 59, 60, 65, 67, 69, 71, 75, 76, 78, 80, 84, 85, 88, 89, 92, 95, 97, 98, 103, 105, 108, 110, 113, 114, 118, 120, 124, 126, 128, 129, 133, 134, 136, 139
(list; graph; listen)
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OFFSET
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0,4
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LINKS
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Daniel Forgues, Table of n, a(n) for n=0..100000
K. Matthews, Computing the prime-power factorization of n!
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MAPLE
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with(numtheory):with(combinat):a:=proc(n) if n=0 then 0 else bigomega(numbperm(n)) fi end: seq(a(n), n=0..63); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 11 2008
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MATHEMATICA
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Array[Plus@@Last/@FactorInteger[ #! ]&, 5!, 0] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 10 2009]
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PROGRAM
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(PARI) v=[]; for(n=1, 200, v=concat(v, bigomega(n!))); v
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CROSSREFS
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a(n) = a(n-1)+A001222(n).
A027746(a(A000040(n))+1) = A000040(n), A082288(a(n)+1) = n.
Cf. A001221(n!) = omega(n!) = pi(n) = A000720(n).
Adjacent sequences: A022556 A022557 A022558 this_sequence A022560 A022561 A022562
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KEYWORD
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nonn,new
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AUTHOR
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Karen E. Wandel (kw29(AT)evansville.edu)
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EXTENSIONS
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Typo corrected by Daniel Forgues (squid(AT)zensearch.com), Nov 16 2009
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