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 A175493 a(n) = Product_{k=1..n} k^d(k), where d(k) = number of divisors of k. 2
 1, 4, 36, 2304, 57600, 74649600, 3657830400, 14982473318400, 10922223049113600, 109222230491136000000, 13215889889427456000000, 39462435755592152776704000000, 6669151642695073819262976000000, 256202129505773955840806486016000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = a(n-1)*A062758(n). a(n) = Product_{k=1..n} k^floor(n/k) * (floor(n/k))!. LINKS Michael S. Branicky, Table of n, a(n) for n = 1..117 MATHEMATICA f[n_] := Product[ k^DivisorSigma[0, k], {k, n}]; Array[f, 15] (* Robert G. Wilson v, Jun 11 2010 *) PROG (Python) from sympy import divisor_count from itertools import count, islice def agen(): an = 1 for k in count(2): yield an an *= k**divisor_count(k) print(list(islice(agen(), 14))) # Michael S. Branicky, May 03 2022 (PARI) a(n) = prod(k=1, n, k^numdiv(k)); \\ Michel Marcus, May 03 2022 CROSSREFS Cf. A062758. Cf. A174939 (sum instead of product). Sequence in context: A152287 A086857 A174864 * A179870 A001152 A349848 Adjacent sequences: A175490 A175491 A175492 * A175494 A175495 A175496 KEYWORD nonn AUTHOR Leroy Quet, May 30 2010 EXTENSIONS a(6) onwards from Robert G. Wilson v and Jon E. Schoenfield, Jun 11 2010 a(14) and beyond from Michael S. Branicky, May 03 2022 STATUS approved

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Last modified September 27 17:53 EDT 2023. Contains 365714 sequences. (Running on oeis4.)