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 A323444 Sum of exponents in prime-power factorization of Product_{k=0..n} binomial(n,k) (A001142). 0
 0, 0, 1, 2, 6, 6, 11, 10, 23, 28, 33, 28, 45, 38, 44, 50, 86, 74, 96, 82, 106, 110, 114, 96, 147, 150, 153, 182, 211, 184, 215, 186, 281, 280, 279, 278, 347, 308, 306, 304, 380, 336, 374, 328, 368, 408, 403, 352, 489, 482, 524, 516, 559, 498, 596, 586, 686, 674 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Also sum of exponents in prime-power factorization of hyperfactorial(n) / superfactorial(n). LINKS Table of n, a(n) for n=0..57. Jeffrey C. Lagarias, Harsh Mehta, Products of binomial coefficients and unreduced Farey fractions, arXiv:1409.4145 [math.NT], 2014. Eric Weisstein's World of Mathematics, Hyperfactorial Eric Weisstein's World of Mathematics, Superfactorial Index entries for sequences related to factorial numbers Index entries for sequences computed from exponents in factorization of n FORMULA a(n) = A303281(n) - A303279(n), for n > 0. a(n) = A001222(A001142(n)). EXAMPLE a(4) = 6 because C(4,0)*C(4,1)*C(4,2)*C(4,3)*C(4,4) = 2^5 * 3^1 and 5 + 1 = 6, where C(n,k) is the binomial coefficient. MATHEMATICA Array[Sum[PrimeOmega@ Binomial[#, k], {k, 0, #}] &, 57] (* Michael De Vlieger, Jan 19 2019 *) PROG (PARI) a(n) = sum(k=0, n, bigomega(binomial(n, k))); (PARI) a(n) = my(t=0); sum(k=1, n, my(b=bigomega(k)); t+=b; k*b-t); (PARI) first(n) = my(res = List([0]), r=0, t=0, b=0); for(k=1, n, b=bigomega(k); t += b; r += k*b-t; listput(res, r)); res \\ adapted from Daniel Suteu \\ David A. Corneth, Jan 16 2019 CROSSREFS Cf. A000178, A001142, A001222, A002109, A004788, A007318, A022559, A303279, A303281. Sequence in context: A290701 A200579 A200809 * A099027 A306925 A134466 Adjacent sequences: A323441 A323442 A323443 * A323445 A323446 A323447 KEYWORD nonn AUTHOR Daniel Suteu, Jan 15 2019 STATUS approved

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Last modified June 15 03:12 EDT 2024. Contains 373402 sequences. (Running on oeis4.)