A008881 a(n) = Product_{j=0..5} floor((n+j)/6).

0, 0, 0, 0, 0, 0, 1, 2, 4, 8, 16, 32, 64, 96, 144, 216, 324, 486, 729, 972, 1296, 1728, 2304, 3072, 4096, 5120, 6400, 8000, 10000, 12500, 15625, 18750, 22500, 27000, 32400, 38880, 46656, 54432, 63504, 74088, 86436, 100842, 117649, 134456, 153664, 175616, 200704

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

For n >= 6, a(n) is the maximal product of 6 positive integers with sum n. - Wesley Ivan Hurt, Jun 29 2022

The maximal product of k positive variables when their sum is equal to s is obtained when each term = s/k; hence, a(6m) = m^6 (A001014). - Bernard Schott, Jul 28 2022

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,5,-10,5,0,0,0,-10,20,-10,0,0,0,10,-20,10,0,0,0,-5,10,-5,0,0,0,1,-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), this sequence (k=6), A009641 (k=7), A009694 (k=8), A009714 (k=9), A354600 (k=10).

Cf. A001014 (6th power), A008588 (multiples of 6), A013664.

Programs

GAP

List([0..50], n-> Product([0..5], j-> Int((n+j)/6))); # G. C. Greubel, Sep 13 2019

Magma

[(&*[Floor((n+j)/6): j in [0..5]]): n in [0..50]]; // G. C. Greubel, Sep 13 2019

Maple

seq( mul( floor((n+i)/6), i=0..5 ), n=0..80);

Mathematica

Product[Floor[(Range[51]+j-2)/6], {j,6}] (* G. C. Greubel, Sep 13 2019 *)

PARI

vector(50, n, prod(j=0,5, (n+j)\6) ) \\ G. C. Greubel, Sep 13 2019

Sage

[product(floor((n+j)/6) for j in (0..5)) for n in (0..50)] # G. C. Greubel, Sep 13 2019

Formula

Sum_{n>=6} 1/a(n) = 1 + zeta(6). - Amiram Eldar, Jan 10 2023