OFFSET
1,1
COMMENTS
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Plot p^e | a(n) at (x,y) = (n,pi(p)), n = 1..1500, pi = A000720, with a color function indicating exponent e = 1 in black, e = 2 = red, e = 3 = orange, ..., maximum e in magenta. The indicator bar below the image represents squarefree a(n) in green, a(n) in A332785 in blue, and a(n) in A286708 in violet.
EXAMPLE
Table showing select values of a(n):
---------------------------------------------------------------
1 36 = 2^2 * 3^2 {36}
2 42 = 2 * 3 * 7 {36}
3 48 = 2^4 * 3 {36}
4 54 = 2 * 3^3 {36}
5 60 = 2^2 * 3 * 5 {36}
6 66 = 2 * 3 * 11 {36}
7 72 = 2^3 * 3^2 {36, 72}
8 78 = 2 * 3 * 13 {36, 72}
9 84 = 2^2 * 3 * 7 {36, 72}
14 108 = 2^2 * 3^3 {36, 72, 108}
17 120 = 2^3 * 3 * 5 {36, 72, 100, 108}
24 150 = 2 * 3 * 5^2 {36, 72, 100, 108, 144}
MATHEMATICA
rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
Reap[Do[m = 1; k = 0;
While[Nor[k == 2, m == n + 1],
If[And[Divisible[n, #], Divisible[m, #^2], ! PrimePowerQ[m] ] &[
rad[m]], k++]; m++];
If[k == 2, Sow[n]], {n, 2^10}] ][[-1, 1]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Oct 06 2024
STATUS
approved