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 A342091 a(n) is the least number k such that k! has n distinct exponents in its prime factorization. 5
 1, 2, 4, 6, 10, 15, 22, 33, 44, 55, 68, 85, 102, 119, 145, 174, 203, 232, 261, 296, 333, 370, 410, 451, 492, 533, 590, 656, 708, 767, 826, 885, 944, 1005, 1072, 1143, 1207, 1278, 1422, 1455, 1562, 1652, 1778, 1917, 2032, 2134, 2235, 2328, 2425, 2540, 2682, 2831, 2929 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS After n=0, first differs from A073818 at n = 27. a(n) is the least k such that A071625(k!) = A071626(k) = n. Is this sequence strictly increasing? LINKS Amiram Eldar, Table of n, a(n) for n = 0..2109 (terms below 10^7) Paul Erdős, Miscellaneous problems in number theory, Proceedings of the Eleventh Manitoba Conference on Numerical Mathematics and Computing (Winnipeg, Man., 1981), Congr. Numer., Vol. 34 (1982), pp. 25-45. EXAMPLE a(1) = 2 since 2! = 2^1 is the least factorial with a single exponent (1) in its prime factorization. a(2) = 4 since 4! = 24 = 2^3 * 3^1 is the least factorial with 2 distinct exponents (1 and 3) in its prime factorization. a(3) = 6 since 6! = 720 = 2^4 * 3^2 * 5^1 is the least factorial with 3 distinct exponents (1, 2 and 4) in its prime factorization. MATHEMATICA f[1] = 0; f[n_] := Length @ Union[FactorInteger[n!][[;; , 2]]]; seq[max_] := Module[{s = Table[0, {max}], n = 1, c = 0}, While[c < max, i = f[n] + 1; If[i <= max && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[50] CROSSREFS Cf. A000142, A071625, A071626, A073818, A133924, A336616, A336619, A336867, A336868. Sequence in context: A086182 A035294 A073818 * A239288 A306145 A143184 Adjacent sequences: A342088 A342089 A342090 * A342092 A342093 A342094 KEYWORD nonn AUTHOR Amiram Eldar, Feb 27 2021 STATUS approved

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Last modified September 17 17:26 EDT 2024. Contains 375990 sequences. (Running on oeis4.)