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
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).
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
(Sage) [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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved