VOOZH about

URL: https://oeis.org/A008881

⇱ A008881 - OEIS

login
A008881
a(n) = Product_{j=0..5} floor((n+j)/6).
12
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
0,8
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
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).
FORMULA
Sum_{n>=6} 1/a(n) = 1 + zeta(6). - Amiram Eldar, Jan 10 2023
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 *)
PROG
(PARI) vector(50, n, prod(j=0, 5, (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
(SageMath) [product(floor((n+j)/6) for j in (0..5)) for n in (0..50)] # G. C. Greubel, Sep 13 2019
(GAP) List([0..50], n-> Product([0..5], j-> Int((n+j)/6))); # G. C. Greubel, Sep 13 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), 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.
Sequence in context: A323097 A272985 A318588 * A208743 A335853 A247213
KEYWORD
nonn,easy
STATUS
approved