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A252796 Smallest of n consecutive integers whose product is divisible by at least n distinct prime factors. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A091605 A145468 A125554 * A083130 A083129 A110160

Adjacent sequences:  A252793 A252794 A252795 * A252797 A252798 A252799

KEYWORD

nonn

AUTHOR

Lior Manor, Dec 22 2014

STATUS

approved

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Last modified July 10 00:25 EDT 2020. Contains 335570 sequences. (Running on oeis4.)