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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
OFFSET
1,1
COMMENTS
a(n) <= A002110(n) - n + 1.
a(n) + n - 1 = A252797(n).
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
Sequence in context: A145468 A125554 A345867 * A083130 A083129 A365090
KEYWORD
nonn
AUTHOR
Lior Manor, Dec 22 2014
STATUS
approved