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A066197 Squarefree kernel of (n*prime(n))*(n+prime(n)). 1

%I #18 Feb 05 2019 03:14:45

%S 6,30,30,154,110,1482,714,114,138,11310,14322,1554,3198,34314,43710,

%T 7314,38114,28914,109478,64610,144102,175538,202354,60342,59170,

%U 333502,40170,22470,436218,484770,622046,42706,768570,817598,239890,169422

%N Squarefree kernel of (n*prime(n))*(n+prime(n)).

%H Charles R Greathouse IV, <a href="/A066197/b066197.txt">Table of n, a(n) for n = 1..10000</a>

%H Ivars Peterson, <a href="http://www.maa.org/mathland/mathtrek_12_8.html">The Amazing ABC Conjecture</a>

%H M. Waldschmidt, <a href="https://arxiv.org/abs/math/0312440">Open Diophantine problems</a>, arXiv:math/0312440 [math.NT], 2003-2004.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/abcConjecture.html">ABC Conjecture</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Abc_conjecture">abc conjecture</a>

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

%e 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.

%t sfk[n_] := Times @@ FactorInteger[n][[All, 1]];

%t a[n_] := sfk[n Prime[n] (n+Prime[n])];

%t Array[a, 40] (* _Jean-François Alcover_, Feb 04 2019 *)

%o (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

%o (Haskell)

%o a066197 n = a007947 $ a033286 n * a014688 n

%o -- _Reinhard Zumkeller_, Jul 24 2013

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Dec 15 2001

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)