A384063 Partial sums of A172471.

0, 1, 3, 5, 7, 10, 13, 16, 20, 24, 28, 32, 36, 41, 46, 51, 56, 61, 67, 73, 79, 85, 91, 97, 103, 110, 117, 124, 131, 138, 145, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 233, 242, 251, 260, 269, 278, 287, 296, 305, 315, 325, 335, 345, 355, 365, 375, 385, 395, 405, 415, 426, 437

Offset: 0

Author

Hoang Xuan Thanh, May 18 2025

Keywords

• nonn

Links

• Hoang Xuan Thanh, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A172471, A173196, A000217.

Programs

Mathematica

Accumulate[Floor[Sqrt[2*Range[0, 100]]]] (* Paolo Xausa, Jun 04 2025 *)

PARI

a(n) = sum(k=1, n, sqrtint(2*k)); \\ Michel Marcus, May 23 2025

Formula

a(n) = m*n - floor((m-1)*(m+3)*(2m-1)/12), where m = A172471(n).

a(n) = m*n - A000217(m-1) - 2*A173196(m-1), where m = A172471(n).