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

1,1

Links

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

Example

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.

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 *)

Crossrefs

Cf. A000142.

Sequence in context: A144653 A276782 A227210 * A349687 A090979 A050508

Adjacent sequences: A177439 A177440 A177441 * A177443 A177444 A177445

Keyword

nonn

Author

Jeff Burch, May 08 2010

Extensions

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

Status

approved