A216324 One half of the radical (squarefree kernel) of the abc-triples (a=1, b(n) = A216323(n), c(n) = 1 + b(n)).

3, 21, 21, 15, 105, 33, 51, 57, 195, 195, 273, 465, 205, 285, 987, 105, 1155, 897, 651, 1365, 105, 357, 1185, 615, 715, 665, 2345, 4395, 2037, 1155, 3003, 897, 1239, 3255, 2667, 8463, 5691, 7755, 2415, 4305, 11985, 4123

Offset: 1

Author

Wolfdieter Lang, Sep 24 2012

Keywords

• nonn

Comments

See a comment on A216323 for the definition of an abc-triple, radical r and quality q which is always > 1 by this definition. There also a link is given.

Examples

			2*105 = 2*a(21) = r(1,4374,4375) = 1*6*35 = 210.
		

Links

• Wolfdieter Lang, Maple program for radical of a*b*(a+b) .

Crossrefs

Cf. A216323.

Programs

Maple

read "radabc.txt": [seq(radabc(1,A216324(n)),n=1..42)]/2;
(with the above given link with the maple text file)

Mathematica

rad[n_] := Times @@ Transpose[FactorInteger[n]][[1]]; a = 1; Table[t = {}; mx = 10^n; Do[c = a + b; If[c < mx && GCD[a, b] == 1 && Log[c] > Log[rad[a*b*c]], AppendTo[t, rad[b*c]/2]], {b, a, mx - a}], {n, 5}]; t (* T. D. Noe, Sep 24 2012 *)

Formula

a(n) = r(1,b(n),b(n)+1) with b(n) = A216323(n), n>=1, and r(a,b,c) is the radical, also known as squarefree kernel, of a*b*c.