OFFSET
1,1
COMMENTS
The smallest k such that k > p^2 such that p is prime and rad(k) | p is p^3.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..32768
Michael De Vlieger, Scatterplot of a(n), m^2, and b(n), n = 1..2^14, where b(n) = A362044(n) is shown in blue, m^2 in black, and a(n) in red.
EXAMPLE
a(1) = 48 since m = 6 and the smallest k > m^2 such that rad(k) | 6 is 48. This is to say, the number that follows 6^2 in A003586 is 48.
a(2) = 80 since m = 10 and the smallest k > m^2 such that rad(k) | 10 is 125. This is to say, the number that precedes 10^2 in A003592 is 125.
Table of n = 1..12, m = A120944(n), m^2, and a(n).
n m m^2 a(n)
---------------------
1 6 36 48
2 10 100 125
3 14 196 224
4 15 225 243
5 21 441 567
6 22 484 512
7 26 676 832
8 30 900 960
9 33 1089 1331
10 34 1156 2048
11 35 1225 1715
12 38 1444 2048
MATHEMATICA
Table[m = k^2 + 1; While[! Divisible[k, Times @@ FactorInteger[m][[All, 1]]], m++]; m, {k, Select[Range[6, 133], And[CompositeQ[#], SquareFreeQ[#]] &]}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Apr 05 2023
STATUS
approved