

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



