A120272 Numerator of Sum_{k=1..n} k/prime(k).

0, 1, 7, 53, 491, 6451, 97723, 1871501, 39642599, 999076987, 31204161323, 1038495626543, 40831064063651, 1770543222362221, 80392862250956443, 3974705945770003271, 220497651647226035923, 13563377141298566879867, 861975691921988407175147, 59980850604601955729416979

Offset: 0

Author

Alexander Adamchuk, Jul 01 2006

Keywords

• frac
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..349

Crossrefs

Denominators are in A002110.

Programs

Magma

[0] cat [Numerator((&+[k/NthPrime(k): k in [1..n]])): n in [1..20]]; // G. C. Greubel, Aug 23 2018

Mathematica

Numerator[Table[Sum[i/Prime[i],{i,1,n}],{n,1,20}]]
Numerator[Accumulate[Table[n/Prime[n],{n,20}]]] (* Harvey P. Dale, Jan 21 2013 *)

PARI

for(n=0,20, print1(if(n==0, 0, numerator(sum(k=1,n, k/prime(k)))), ", ")) \\ G. C. Greubel, Aug 23 2018

Formula

a(n) = A258851(A002110(n)). - Alois P. Heinz, Jun 26 2015

Extensions

a(0)=0 prepended by Alois P. Heinz, Jun 26 2015