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A120271 Numerator of Sum[ 1/(Prime[k]-1), {k,1,n}]. 7

%I

%S 1,3,7,23,121,21,173,1597,17927,127469,129317,43619,44081,44521,

%T 1033223,13538159,395369371,132680013,400467919,402757063,1214947859,

%U 1221110939,50305908619,50529880549,101470376303,509322834499,8691337402883

%N Numerator of Sum[ 1/(Prime[k]-1), {k,1,n}].

%C a(n) are squarefree except for n = 5, 14, 49, ... where squared prime factors are 11, 211, 479, ...

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

%F a(n) = numerator(Sum_{k=1..n} 1/(prime(k)-1)).

%F a(n) = A078456(n) * A135212(n). - _Alexander Adamchuk_, Nov 23 2007

%t Numerator[Table[Sum[1/(Prime[i]-1),{i,1,n}],{n,1,50}]]

%o (PARI) a(n) = numerator(sum(k=1, n, 1/(prime(k)-1))); \\ _Michel Marcus_, Oct 02 2016

%Y Cf. A119686, A006093, A000040.

%Y Cf. A135212, A078456.

%K frac,nonn

%O 1,2

%A _Alexander Adamchuk_, Jul 01 2006

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Last modified July 24 20:26 EDT 2021. Contains 346273 sequences. (Running on oeis4.)