A374730 a(n) = n * binomial(floor(log_2(n)) + 1, 2).

0, 0, 2, 3, 12, 15, 18, 21, 48, 54, 60, 66, 72, 78, 84, 90, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735, 750, 765, 780, 795, 810, 825, 840

Offset

0,3

Links

Table of n, a(n) for n=0..56.

Formula

a(A000079(n)) = A001815(n+1).

a(n) = n * A000217(A000523(n)).

Maple

a := n -> n * binomial(ilog2(n) + 1, 2):
seq(a(n), n = 0..56);  # Peter Luschny, Jul 19 2024

Mathematica

Table[n * Binomial[BitLength[n], 2], {n, 0, 60}] (* Amiram Eldar, Jul 23 2024 *)

Prog

(Python)
def a(n):
    q = n.bit_length() - 1
    return n * q * (q + 1) >> 1
print([a(n) for n in range(61)])
(PARI) a(n) = n * binomial(logint(n, 2) + 1, 2); \\ Michel Marcus, Jul 23 2024

Crossrefs

Cf. A000079, A000217, A000523, A001815.

Sequence in context: A173079 A173903 A154785 * A090512 A076175 A289870

Adjacent sequences: A374727 A374728 A374729 * A374731 A374732 A374733

Keyword

nonn

Author

Darío Clavijo, Jul 17 2024

Status

approved