A374426 a(n) = n*(n + 1)/2 + pi(n), where pi(n) = A000720(n) is the prime counting function.

1, 4, 8, 12, 18, 24, 32, 40, 49, 59, 71, 83, 97, 111, 126, 142, 160, 178, 198, 218, 239, 261, 285, 309, 334, 360, 387, 415, 445, 475, 507, 539, 572, 606, 641, 677, 715, 753, 792, 832, 874, 916, 960, 1004, 1049, 1095, 1143, 1191, 1240, 1290, 1341, 1393, 1447

Offset

1,2

Links

James C. McMahon, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000217(n) + A000720(n).

a(1) = 1; for n > 1: a(n) = a(n-1) + n + A010051(n).

Mathematica

Table[n(n+1)/2+PrimePi[n], {n, 53}]

Prog

(PARI) a(n) = n*(n+1)/2 + primepi(n); \\ Michel Marcus, Jul 31 2024

Crossrefs

Cf. A000217, A000720, A010051, A256885.

Partial sums of A014683.

Sequence in context: A311635 A049621 A072511 * A156324 A311636 A311637

Adjacent sequences: A374423 A374424 A374425 * A374427 A374428 A374429

Keyword

nonn,new

Author

James C. McMahon, Jul 08 2024

Status

approved