A252796 Smallest of n consecutive integers whose product is divisible by at least n distinct prime factors.

2, 2, 3, 4, 7, 9, 11, 16, 26, 29, 29, 36, 50, 56, 57, 79, 79, 101, 106, 145, 166, 172, 172, 196, 199, 211, 211, 257, 290, 386, 393, 393, 401, 421, 514, 514, 530, 652, 757, 757, 757, 761, 761, 761, 785, 785, 785, 1135, 1225, 1236, 1236, 1373, 1381, 1381, 1601

Offset

1,1

Comments

a(n) <= A002110(n) - n + 1.

a(n) + n - 1 = A252797(n).

Links

Lior Manor, Table of n, a(n) for n = 1..199

Example

a(5) = 7, since the product of the 5 consecutive integers 7..11 is divisible by 5 distinct prime factors, and no smaller set of 5 such consecutive integers exists.

Mathematica

a252796[n_] := Block[{k},
  Table[k = 1; While[i != PrimeNu[Times @@ Range[k, k + i - 1]], k++];
k, {i, n}]]; a252796[55] (* Michael De Vlieger, Dec 22 2014 *)

Crossrefs

Cf. A002110, A252797.

Sequence in context: A145468 A125554 A345867 * A083130 A083129 A365090

Adjacent sequences: A252793 A252794 A252795 * A252797 A252798 A252799

Keyword

nonn

Author

Lior Manor, Dec 22 2014

Status

approved