A009694 a(n) = Product_{i=0..7} floor((n+i)/8).

0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 6561, 8748, 11664, 15552, 20736, 27648, 36864, 49152, 65536, 81920, 102400, 128000, 160000, 200000, 250000, 312500

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

For n >= 8, a(n) is the maximal product of eight positive integers with sum n. - Wesley Ivan Hurt, Jul 08 2022

A quasipolynomial of order 8 and degree 8. - Charles R Greathouse IV, Nov 06 2022

Links

• Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, 0, 0, 0, 7, -14, 7, 0, 0, 0, 0, 0, -21, 42, -21, 0, 0, 0, 0, 0, 35, -70, 35, 0, 0, 0, 0, 0, -35, 70, -35, 0, 0, 0, 0, 0, 21, -42, 21, 0, 0, 0, 0, 0, -7, 14, -7, 0, 0, 0, 0, 0, 1, -2, 1).

Crossrefs

Maximal product of k positive integers with sum n, for k = 2..10: A002620 (k=2), A006501 (k=3), A008233 (k=4), A008382 (k=5), A008881 (k=6), A009641 (k=7), this sequence (k=8), A009714 (k=9), A354600 (k=10).

Cf. A001016, A013666.

Programs

Mathematica

Table[Product[Floor[(n+i)/8],{i,0,7}],{n,0,40}] (* Harvey P. Dale, Nov 13 2013 *)

PARI

a(n) = prod(i=0, 7, (n+i)\8); \\ Michel Marcus, Jul 14 2022

Formula

a(8*n) = n^8 (A001016). - Bernard Schott, Nov 06 2022

a(n) = n^8/8^8 + O(n^6). - Charles R Greathouse IV, Nov 06 2022

Sum_{n>=8} 1/a(n) = 1 + zeta(8). - Amiram Eldar, Jan 10 2023