A333644 - OEIS

%I #8 Nov 18 2023 21:03:53

%S 2,7,14,26,39,62,81,112,142,187,220,287,330,395,460,544,605,712,781,

%T 904,1001,1116,1201,1376,1486,1633,1766,1945,2056,2279,2408,2623,2798,

%U 3001,3180,3482,3641,3876,4091,4406,4587,4924,5117,5432,5717,6004,6217,6668,6914,7285

%N a(n) = Sum_{k=1..n} floor(n/k) * prime(k).

%C Partial sums of A007445.

%F G.f.: (1/(1 - x)) * Sum_{k>=1} prime(k) * x^k / (1 - x^k).

%t Table[Sum[Floor[n/k] Prime[k], {k, n}], {n, 50}]

%o (PARI) a(n) = sum(k=1, n, (n\k)*prime(k)); \\ _Michel Marcus_, Mar 31 2020

%Y Cf. A000040, A007445, A024916, A333471.

%K nonn

%O 1,1

%A _Ilya Gutkovskiy_, Mar 31 2020