A009714 a(n) = Product_{i=0..8} floor((n+i)/9).

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 768, 1152, 1728, 2592, 3888, 5832, 8748, 13122, 19683, 26244, 34992, 46656, 62208, 82944, 110592, 147456, 196608, 262144, 327680, 409600, 512000, 640000, 800000, 1000000, 1250000, 1562500

Offset

0,11

Comments

For n >= 9, a(n) is the maximal product of 9 positive integers with sum n. - Wesley Ivan Hurt, Jul 08 2022

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, 0, 0, 0, 0, 8, -16, 8, 0, 0, 0, 0, 0, 0, -28, 56, -28, 0, 0, 0, 0, 0, 0, 56, -112, 56, 0, 0, 0, 0, 0, 0, -70, 140, -70, 0, 0, 0, 0, 0, 0, 56, -112, 56, 0, 0, 0, 0, 0, 0, -28, 56, -28, 0, 0, 0, 0, 0, 0, 8, -16, 8, 0, 0, 0, 0, 0, 0, -1, 2, -1).

Formula

a(9*n) = n^9. - Bernard Schott, Nov 20 2022

a(9*n+j) = n^(9-j)*(n+1)^j for 0 <= j <= 8. - Robert Israel, Nov 21 2022

Sum_{n>=9} 1/a(n) = 1 + zeta(9). - Amiram Eldar, Jan 10 2023

Mathematica

A009714[n_] := Product[Floor[(n + i)/9], {i, 0, 8}];
Array[A009714, 50, 0] (* Paolo Xausa, Aug 21 2024 *)

Prog

(PARI) a(n) = prod(k=0, 8, floor((n+k)/9)); \\ Georg Fischer, Nov 07 2019

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), A009694 (k=8), this sequence (k=9), A354600 (k=10).

Cf. A001017 (n^9, a subsequence), A013667.

Sequence in context: A281938 A242350 A115213 * A051535 A008862 A145116

Adjacent sequences: A009711 A009712 A009713 * A009715 A009716 A009717

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved