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A176383 Triangle of the powers of the prime factorization of n! in row n. 1
2, 2, 3, 8, 3, 8, 3, 5, 16, 9, 5, 16, 9, 5, 7, 128, 9, 5, 7, 128, 81, 5, 7, 256, 81, 25, 7, 256, 81, 25, 7, 11, 1024, 243, 25, 7, 11, 1024, 243, 25, 7, 11, 13, 2048, 243, 25, 49, 11, 13, 2048, 729, 125, 49, 11, 13, 32768, 729, 125, 49, 11, 13, 32768, 729, 125, 49, 11, 13, 17, 65536 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
Row n contains pi(n) = A000720(n) terms. The exponents are in A115627.
The first column contains the maximum power of 2 dividing n!, the second column the maximum power of 3 dividing n! etc.
LINKS
EXAMPLE
The irregular tables starts with n=2:
2; # =2! = 2
2*3; # =3! = 6
8*3; # =4! = 24
8*3*5; # =5! = 120
16*9*5; # =6!
16*9*5*7; # =7!
128*9*5*7; # =8!
128*81*5*7;
256*81*25*7;
MAPLE
with(numtheory):
b:= proc(n) option remember; `if`(n=1, 1, b(n-1)+
add(i[2]*x^pi(i[1]), i=ifactors(n)[2]))
end:
T:= n->(p->seq(ithprime(i)^coeff(p, x, i), i=1..pi(n)))(b(n)):
seq(T(n), n=2..20); # Alois P. Heinz, Jun 22 2014
MATHEMATICA
T[n_] := List @@ Power @@@ FactorInteger[n!];
Array[T, 20, 2] // Flatten (* Jean-François Alcover, Mar 27 2017 *)
Rest[Flatten[Table[#[[1]]^#[[2]]&/@FactorInteger[n!], {n, 20}]]] (* Harvey P. Dale, Jan 04 2019 *)
PROG
(PARI) a(n)=my(i=2); while(n-primepi(i)>1, n-=primepi(i); i++); p=prime(n-1); p^sum(j=1, log(i)\log(p), i\=p) \\ David A. Corneth, Jun 21 2014
CROSSREFS
Sequence in context: A204197 A238654 A220553 * A100551 A267667 A210190
KEYWORD
nonn,tabf
AUTHOR
Vladimir Shevelev, Apr 16 2010
EXTENSIONS
Arbitrarily defined first 2 terms removed by R. J. Mathar, Apr 23 2010
STATUS
approved

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Last modified June 20 08:48 EDT 2024. Contains 373515 sequences. (Running on oeis4.)