A108753 Difference between the n-th partial sum of the squares (A000330) and the n-th partial sum of the primes (A007504).

-1, 0, 4, 13, 27, 50, 82, 127, 185, 256, 346, 453, 581, 734, 912, 1115, 1345, 1608, 1902, 2231, 2599, 3004, 3450, 3937, 4465, 5040, 5666, 6343, 7075, 7862, 8696, 9589, 10541, 11558, 12634, 13779, 14991, 16272, 17626, 19053, 20555, 22138, 23796, 25539, 27367

Offset: 1

Author

Alexandre Wajnberg, Jun 23 2005

Keywords

• base
• easy
• sign

Comments

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

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000330, A007504.

Partial sums of A073497.

Programs

Mathematica

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

Extensions

Edited and extended by Robert G. Wilson v, Jun 25 2005