

A360316


a(n) is the smallest k such that k!'s prime(n)smooth part is less than its prime(n+1)rough part.


0



3, 21, 47, 111, 186, 293, 437, 619, 830, 1070, 1358, 1662, 2019, 2428, 2903, 3373, 3908, 4493, 5113, 5791, 6506, 7325, 8150, 9043, 9942, 10929, 11983, 13089, 14303, 15591, 16845, 18143, 19535, 21003, 22488, 24046, 25693, 27333, 29119, 30905, 32741, 34764, 36734
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OFFSET

1,1


LINKS



EXAMPLE

For n=1, the prime(1)smooth part of k! (i.e., the 2smooth part) is the part whose prime factors are 2's; the prime(2)rough part (i.e., the 3rough part) is the odd part. For k = 1..3, we have
k k! 2smooth part 3rough part
   
1 1 1 = 1
2 2 2 > 1
3 6 2 < 3
so a(1)=3.
Similarly, for n=2, we have
k 3smooth part 5rough part
  
1 1 = 1
2 2 > 1
3 6 > 1
4 24 > 1
5 24 > 5
. . . .
. . . .
18 429981696 > 14889875
19 429981696 > 282907625
20 1719926784 > 1414538125
21 5159780352 < 9901766875
so a(2)=21.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



