OFFSET
0,5
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = A136567(n!). - Amiram Eldar, Aug 08 2024
EXAMPLE
14! is factored into primes as 2^11 * 3^5 * 5^2 * 7^2 * 11^1 * 13^1. The exponent 1 and 2 each occur more than once. So the exponents occurring only once each are 5 and 11. Therefore a(14) = 2.
MAPLE
A133924 := proc(n) local ifs, a, i ; if n <= 1 then RETURN(0) ; else ifs := ifactors(n!)[2] ; ifs := sort([seq(op(2, i), i=ifs)]) ; a :=0 ; for i from 1 to nops(ifs) do if i = 1 or op(i, ifs) <> op(i-1, ifs) then if i=nops(ifs) or op(i, ifs) <> op(i+1, ifs) then a := a+1 ; fi ; fi ; od: RETURN(a) ; fi ; end: seq(A133924(n), n=0..120) ; # R. J. Mathar, Jan 30 2008
MATHEMATICA
ne1[n_]:=Count[Tally[Transpose[FactorInteger[n!]][[2]]], _?(Last[#] == 1&)]; Join[{0, 0}, Array[ne1, 110, 2]] (* Harvey P. Dale, Aug 21 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Jan 07 2008
EXTENSIONS
More terms from R. J. Mathar, Jan 30 2008
STATUS
approved