A024850 - OEIS

A024850

Let c(k) denote the k-th composite number and p(k) the k-th prime number; then a(n) = Sum_{i=n*(n-1)/2+1 .. n*(n+1)/2} c(i) - Sum_{i=1..n} p(i).

%I #19 Jul 26 2019 21:29:08

%S 2,9,21,46,84,135,206,308,429,583,772,987,1265,1552,1906,2308,2767,

%T 3278,3840,4478,5201,5956,6783,7704,8706,9777,10976,12241,13591,14985,

%U 16546,18230,20019,21862,23824,25907,28111,30474,32897,35482,38208,41125,44159,47239,50516,53944

%N Let c(k) denote the k-th composite number and p(k) the k-th prime number; then a(n) = Sum_{i=n*(n-1)/2+1 .. n*(n+1)/2} c(i) - Sum_{i=1..n} p(i).

%F a(n) = A072475(n) - A007504(n) [corrected by _Sean A. Irvine_, Jul 26 2019].

%e a(1) = 4 - 2 = 2.

%e a(2) = 6 + 8 - 2 - 3 = 9.

%e a(3) = 9 + 10 + 12 - 2 - 3 - 5 = 21.

%Y Cf. A071411.

%K nonn

%O 1,1

%A _Amarnath Murthy_ and _Benoit Cloitre_, Jun 23 2002

%E a(7) and a(8) corrected and more terms from _Sean A. Irvine_, Jul 26 2019