A108753 - OEIS

%I #12 Jul 14 2022 17:24:45

%S -1,0,4,13,27,50,82,127,185,256,346,453,581,734,912,1115,1345,1608,

%T 1902,2231,2599,3004,3450,3937,4465,5040,5666,6343,7075,7862,8696,

%U 9589,10541,11558,12634,13779,14991,16272,17626,19053,20555,22138,23796,25539,27367

%N Difference between the n-th partial sum of the squares (A000330) and the n-th partial sum of the primes (A007504).

%C Numbers congruent to {0, 3, 8, 11} mod 12.

%H Harvey P. Dale, <a href="/A108753/b108753.txt">Table of n, a(n) for n = 1..1000</a>

%e a(4) = A000330(4) - A007504(4) = (1 + 4 + 9 + 16) - (2 + 3 + 5 + 7) = 30 - 17 = 13.

%t f[n_] := n(n + 1)(2n + 1)/6 - Sum[Prime[i], {i, n}]; Table[ f[n], {n, 15}] (* _Robert G. Wilson v_, Jun 25 2005 *)

%t #[[1]]-#[[2]]&/@With[{nn=50},Thread[{Accumulate[Range[nn]^2], Accumulate[ Prime[ Range[nn]]]}]] (* _Harvey P. Dale_, May 07 2013 *)

%Y Cf. A000330, A007504.

%Y Partial sums of A073497.

%K base,easy,sign

%O 1,3

%A _Alexandre Wajnberg_, Jun 23 2005

%E Edited and extended by _Robert G. Wilson v_, Jun 25 2005