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A133924 a(n) = number of exponents occurring only once each in the prime factorization of n!. 2
0, 0, 1, 0, 2, 1, 3, 2, 2, 2, 4, 3, 3, 3, 2, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 6, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..104.

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

Cf. A071626.

Sequence in context: A035191 A276166 A177062 * A023135 A191654 A205784

Adjacent sequences:  A133921 A133922 A133923 * A133925 A133926 A133927

KEYWORD

nonn

AUTHOR

Leroy Quet, Jan 07 2008

EXTENSIONS

More terms from R. J. Mathar, Jan 30 2008

STATUS

approved

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Last modified February 24 07:50 EST 2018. Contains 299599 sequences. (Running on oeis4.)