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A008881
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a(n) = Product_{j=0..5} floor((n+j)/6).
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12
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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
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OFFSET
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0,8
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COMMENTS
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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
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LINKS
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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).
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FORMULA
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Sum_{n>=6} 1/a(n) = 1 + zeta(6). - Amiram Eldar, Jan 10 2023
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MAPLE
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seq( mul( floor((n+i)/6), i=0..5 ), n=0..80);
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MATHEMATICA
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Product[Floor[(Range[51]+j-2)/6], {j, 6}] (* G. C. Greubel, Sep 13 2019 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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