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

Author

James C. McMahon, Jul 08 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A000217, A000720, A010051, A256885.

Partial sums of A014683.

Programs

Mathematica

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

PARI

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

Formula

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

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