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 A346418 a(n) is the exponent of the largest power of n that divides the least common multiple of {1,2,...,n} (A003418). a(1) = 1. 3
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,30 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Paul Erdős, Problem 10192, The American Mathematical Monthly, Vol. 99, No. 1 (1992), p. 61; An Arithmetic Function of Modest Size, solution to problem 10192 by Richard Stong, ibid., Vol. 104, No. 1 (1997), pp. 69-70. FORMULA a(n) <= omega(n), and a(n) < omega(n) whenever omega(n) > 1. Max_{k=2..n} a(k) ~ log(n)/(log(log(n)) + o(1)) (Erdős, 1992). EXAMPLE a(2) = 1 since A003418(2) = 2, and 2^1|A003418(2). a(30) = 2 since A003418(30) = 2329089562800 = 30^2 * 2587877292, and 30^2|A003418(30). MATHEMATICA a[1] = 1; a[n_] := IntegerExponent[LCM @@ Range[n], n]; Array[a, 100] PROG (PARI) a(n) = if (n==1, 1, valuation(lcm([1..n]), n)); \\ Michel Marcus, Jul 17 2021 CROSSREFS Cf. A001221, A003418, A011776. Sequence in context: A054977 A272901 A078315 * A288120 A156264 A249770 Adjacent sequences: A346415 A346416 A346417 * A346419 A346420 A346421 KEYWORD nonn AUTHOR Amiram Eldar, Jul 16 2021 STATUS approved

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Last modified May 30 12:02 EDT 2023. Contains 363050 sequences. (Running on oeis4.)