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Numerator of Sum_{k=1..n} k/prime(k).
2

%I #22 Sep 08 2022 08:45:25

%S 0,1,7,53,491,6451,97723,1871501,39642599,999076987,31204161323,

%T 1038495626543,40831064063651,1770543222362221,80392862250956443,

%U 3974705945770003271,220497651647226035923,13563377141298566879867,861975691921988407175147,59980850604601955729416979

%N Numerator of Sum_{k=1..n} k/prime(k).

%H Harvey P. Dale, <a href="/A120272/b120272.txt">Table of n, a(n) for n = 0..349</a>

%F a(n) = A258851(A002110(n)). - _Alois P. Heinz_, Jun 26 2015

%t Numerator[Table[Sum[i/Prime[i],{i,1,n}],{n,1,20}]]

%t Numerator[Accumulate[Table[n/Prime[n],{n,20}]]] (* _Harvey P. Dale_, Jan 21 2013 *)

%o (PARI) for(n=0,20, print1(if(n==0, 0, numerator(sum(k=1,n, k/prime(k)))), ", ")) \\ _G. C. Greubel_, Aug 23 2018

%o (Magma) [0] cat [Numerator((&+[k/NthPrime(k): k in [1..n]])): n in [1..20]]; // _G. C. Greubel_, Aug 23 2018

%Y Denominators are in A002110.

%K frac,nonn

%O 0,3

%A _Alexander Adamchuk_, Jul 01 2006

%E a(0)=0 prepended by _Alois P. Heinz_, Jun 26 2015