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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 Alois P. Heinz, Rows n = 2..300, flattened 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 Cf. A000142, A000720. Sequence in context: A204197 A238654 A220553 * A100551 A267667 A210190 Adjacent sequences: A176380 A176381 A176382 * A176384 A176385 A176386 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.)