|
| |
|
|
A022559
|
|
Sum of exponents in prime-power factorization of n!.
|
|
16
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
COMMENTS
| For n > 0, partial sums of bigomega (A001222): number of prime divisors (counted with multiplicity). Subsequence of primes: 2, 5, 7, 11, 13, 19, 29, 41, 47, 59, 67, 71, 89, 97, 103, 113, 139, 151, 179, 191, 211, 229, 239, 251, 263, .... [Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 10 2010]
|
|
|
LINKS
| Daniel Forgues, Table of n, a(n) for n = 0..100000
K. Matthews, Computing the prime-power factorization of n!
|
|
|
FORMULA
| a(n) = a(n-1)+A001222(n).
A027746(a(A000040(n))+1) = A000040(n). A082288(a(n)+1) = n.
A001221(n!) = omega(n!) = pi(n) = A000720(n).
a(n) = SUM[i=1..n] A001222(i) = SUM[i=1..n] bigomega(i) = SUM[i=1..n] {Number of prime divisors of i (counted with multiplicity)}. [Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 10 2010]
a(n) = n log log n + B_2 * n + o(n), with B_2 = A083342. [Charles R Greathouse IV, Jan 11 2012]
|
|
|
MAPLE
| 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
|
|
|
MATHEMATICA
| Array[Plus@@Last/@FactorInteger[ #! ]&, 5!, 0] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 10 2009]
f[n_] := If[n <= 1, 0, Total[FactorInteger[n]][[2]]]; Accumulate[Array[f, 100, 0]] (* T. D. Noe, Apr 11 2011 *)
|
|
|
PROG
| (PARI) a(n)=bigomega(n!)
(PARI) k=0; vector(n, i, k+=bigomega(i))
|
|
|
CROSSREFS
| Cf. A001222, A013939, A046660, A144494, A115627.
Sequence in context: A111040 A191324 A147807 * A049781 A174090 A076697
Adjacent sequences: A022556 A022557 A022558 * A022560 A022561 A022562
|
|
|
KEYWORD
| nonn,nice
|
|
|
AUTHOR
| Karen E. Wandel (kw29(AT)evansville.edu)
|
|
|
EXTENSIONS
| Typo corrected by Daniel Forgues (squid(AT)zensearch.com), Nov 16 2009
|
| |
|
|
