A374896 Array read by falling antidiagonals: T(n,k) = denominator(Sum_{x>0} (x^n)/(k^x)); n >= 0 and k >= 2.
1, 2, 1, 3, 4, 1, 4, 9, 2, 1, 5, 16, 27, 8, 1, 6, 25, 32, 27, 1, 1, 7, 36, 125, 128, 81, 4, 1, 8, 49, 27, 625, 128, 243, 4, 1, 9, 64, 343, 216, 3125, 512, 243, 16, 1, 10, 81, 256, 2401, 81, 3125, 1024, 729, 1, 1, 11, 100, 729, 2048, 16807, 972, 15625, 4096, 2187, 4, 1
Offset: 0
Examples
Array begins: +-----+-----------------------------------------------+ | n\k | 2 3 4 5 6 7 8 ... | +-----+-----------------------------------------------+ | 0 | 1 2 3 4 5 6 7 ... | | 1 | 1 4 9 16 25 36 49 ... | | 2 | 1 2 27 32 125 27 343 ... | | 3 | 1 8 27 128 625 216 2401 ... | | 4 | 1 1 81 128 3125 81 16807 ... | | 5 | 1 4 243 512 3125 972 117649 ... | | 6 | 1 4 243 1024 15625 486 823543 ... | | 7 | 1 16 729 4096 78125 11664 823543 ... | | 8 | 1 1 2187 2048 390625 2187 5764801 ... | | ... | ... ... ... ... ... ... ... ... | +-----+-----------------------------------------------+
Programs
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PARI
T(n,k) = denominator(polylog(-n, 1/k)); matrix(7,7,n, k, T(n-1,k+1)) \\ Michel Marcus, Aug 04 2024