A327909 a(n) is the smallest start of a run of n or more integers having a prime factor greater than n.

2, 5, 13, 19, 55, 65, 113, 151, 151, 226, 364, 406, 736, 736, 1057, 1057, 1409, 1409, 2059, 2059, 2313, 2313, 2313, 2313, 2313, 2313, 2313, 6007, 6961, 6961, 10305, 12013, 12013, 12013, 12013, 12013, 12026, 12026, 17501, 17501, 17501, 17501, 20833, 20833

Offset: 1

Author

Jon E. Schoenfield, Oct 06 2019

Keywords

• nonn

Comments

Is a(n) an upper bound on A327265(n)? A327265(n) = a(n) at n = 1, 2, 4, and 9.

Examples

			      |     prime     |
   k  | factorization | gpf(k) | tau(k)
  ----+---------------+--------+-------
  151 |      151      |   151  |   2
  152 |   2^3 * 19    |    19  |   8
  153 |   3^2 * 17    |    17  |   6
  154 |  2 * 7 * 11   |    11  |   8
  155 |    5 * 31     |    31  |   4
  156 | 2^2 * 3 * 13  |    13  |  12
  157 |      157      |   157  |   2
  158 |    2 * 79     |    79  |   4
  159 |    3 * 53     |    53  |   4
		

Links

• Thomas Garrison, Table of n, a(n) for n = 1..369

Crossrefs

Cf. A006530 (greatest prime factor of n).

Cf. A309981, A327265.

Programs

Maple

A:= Vector(100): A[1]:= 2: count:= 1:
B:= Vector(100):
for i from 2 while count < 100 do
  p:= max(numtheory:-factorset(i));
  for j from 1 to min(p-1,100) do
    if B[j] = 0 then B[j]:= i fi
  od;
  for j from p to 100 do
    if B[j] > 0 and B[j] <= i-j and A[j] = 0 then A[j]:= B[j]; count:= count+1; fi
  od;
  if p <= 99 then B[p..100]:= 0 fi;
od:
convert(A,list); # Robert Israel, Jan 23 2023

PARI

a(n) = {my(k=1); x=0; while(xn, x++, x=0)); k-n+1;} \\ Jinyuan Wang, Oct 26 2019