A177442 Smallest a(n) such that the prime factorization of a(n)! contains at least one factor to each exponent between 1 and n.

2, 6, 15, 22, 55, 68, 85, 145, 261, 296, 333, 370, 492, 533, 590, 885, 944, 1005, 1143, 1207, 1278, 2831, 2980, 3048, 3175, 3302, 3429, 3576, 3725, 3874, 4023, 4775, 4966, 7368, 7582, 7805, 8289, 8606, 9036, 9036, 9287, 9599, 9599, 9824, 13902, 14233

Offset: 1

Author

Jeff Burch, May 08 2010

Keywords

• nonn

Examples

			15! = 2^11 * 3^6 * 5^3 * 7^2 * 11 * 13 and is the smallest number whose prime factorization has at least one factor with exponent 1, one factor with exponent 2, and one factor with exponent 3, so a(3)=15.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..276

Crossrefs

Cf. A000142.

Programs

Mathematica

f[n_] := Module[{e = Union[FactorInteger[n!][[;; , 2]]]}, FirstPosition[Differences[e], ?(# > 1 &)][[1]]]; f[2] = f[3] = 1; seq[len] := Module[{s = Table[0, {len}], n = 1, c = 0, i}, While[c < len, n++; i = f[n]; Do[If[s[[j]] == 0, c++; s[[j]] = n], {j, 1, Min[i, len]}]]; s]; seq[40] (* Amiram Eldar, Apr 20 2023 *)

Extensions

Corrected and extended by D. S. McNeil, May 22 2010