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Revision History for A133924

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A133924

a(n) = number of exponents occurring only once each in the prime factorization of n!.
(history; published version)

#7 by Charles R Greathouse IV at Thu Nov 21 12:49:07 EST 2013

MATHEMATICA

ne1[n_]:=Count[Tally[Transpose[FactorInteger[n!]][[2]]], _?(Last[#] == 1&)]; Join[{0, 0}, Array[ne1, 110, 2]] (* From ]] (* _Harvey P. Dale, _, Aug 21 2011 *)

Discussion
Thu Nov 21	12:49	OEIS Server: https://oeis.org/edit/global/2062

#6 by Russ Cox at Fri Mar 30 17:39:26 EDT 2012

	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 (mathar(AT)strw.leidenuniv.nl), _, Jan 30 2008`
	EXTENSIONS	`More terms from _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Jan 30 2008`

Discussion
Fri Mar 30	17:39	OEIS Server: https://oeis.org/edit/global/190

#5 by Harvey P. Dale at Sun Aug 21 08:44:15 EDT 2011

STATUS

editing

approved

#4 by Harvey P. Dale at Sun Aug 21 08:44:08 EDT 2011

MATHEMATICA

ne1[n_]:=Count[Tally[Transpose[FactorInteger[n!]][[2]]], _?(Last[#] == 1&)]; Join[{0, 0}, Array[ne1, 110, 2]] (* From Harvey P. Dale, Aug 21 2011 *)

STATUS

approved

editing

#3 by N. J. A. Sloane at Sat Oct 02 03:00:00 EDT 2010

LINKS

Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> (listed in lieu of email address)

KEYWORD

nonn,new

nonn

#2 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

LINKS

Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> (listed in lieu of email address)

KEYWORD

nonn,new

nonn

AUTHOR

Leroy Quet (qq-quet(AT)mindspring.com), Jan 07 2008

#1 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

	NAME	`a(n) = number of exponents occurring only once each in the prime-factorization of n!.`
	DATA	`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`
	OFFSET	`0,5`
	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 (mathar(AT)strw.leidenuniv.nl), Jan 30 2008`
	CROSSREFS	`Cf. A071626.`
	KEYWORD	`nonn`
	AUTHOR	`Leroy Quet (qq-quet(AT)mindspring.com), Jan 07 2008`
	EXTENSIONS	`More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 30 2008`
	STATUS	`approved`

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Last modified August 18 20:50 EDT 2024. Contains 375284 sequences. (Running on oeis4.)