login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A009694 a(n) = Product_{i=0..7} floor((n+i)/8). 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,10
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).
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
MATHEMATICA
Table[Product[Floor[(n+i)/8], {i, 0, 7}], {n, 0, 40}] (* Harvey P. Dale, Nov 13 2013 *)
PROG
(PARI) a(n) = prod(i=0, 7, (n+i)\8); \\ Michel Marcus, Jul 14 2022
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).
Sequence in context: A252757 A230579 A361937 * A275816 A097000 A285894
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 22 22:43 EST 2024. Contains 370265 sequences. (Running on oeis4.)