A066197 Squarefree kernel of (n*prime(n))*(n+prime(n)).

6, 30, 30, 154, 110, 1482, 714, 114, 138, 11310, 14322, 1554, 3198, 34314, 43710, 7314, 38114, 28914, 109478, 64610, 144102, 175538, 202354, 60342, 59170, 333502, 40170, 22470, 436218, 484770, 622046, 42706, 768570, 817598, 239890, 169422

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Ivars Peterson, The Amazing ABC Conjecture

M. Waldschmidt, Open Diophantine problems, arXiv:math/0312440 [math.NT], 2003-2004.

Eric Weisstein's World of Mathematics, ABC Conjecture

Eric Weisstein's World of Mathematics, Squarefree

Wikipedia, abc conjecture

Formula

a(n) = A007947(A033286(n) * A014688(n)).

Example

For n=20 we have: A = n = 20, B = A000040(20) = 71, C = A + B = 20 + 71 = 91 and A*B*C = 129220 with squarefree kernel a(20) = 64610 = 2*5*7*13*71.

Mathematica

sfk[n_] := Times @@ FactorInteger[n][[All, 1]];
a[n_] := sfk[n Prime[n] (n+Prime[n])];
Array[a, 40] (* Jean-François Alcover, Feb 04 2019 *)

Prog

(PARI) a(n)=my(p=prime(n), f=vecsort(concat(concat(p, factor(n)[, 1]), factor(n+p)[, 1]), , 8)~); prod(i=1, #f, f[i]) \\ Charles R Greathouse IV, Jul 23 2013
(Haskell)
a066197 n = a007947 $ a033286 n * a014688 n
-- Reinhard Zumkeller, Jul 24 2013

Crossrefs

Sequence in context: A351773 A123624 A287733 * A078638 A068510 A147798

Adjacent sequences: A066194 A066195 A066196 * A066198 A066199 A066200

Keyword

nonn

Author

Reinhard Zumkeller, Dec 15 2001

Status

approved