The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A322264 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = denominator of Sum_{d|n} 1/d^k. 1
 1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 8, 9, 4, 1, 1, 16, 27, 16, 5, 1, 1, 32, 81, 64, 25, 1, 1, 1, 64, 243, 256, 125, 18, 7, 1, 1, 128, 729, 1024, 625, 6, 49, 8, 1, 1, 256, 2187, 4096, 3125, 648, 343, 64, 9, 1, 1, 512, 6561, 16384, 15625, 648, 2401, 512, 81, 5, 1, 1, 1024, 19683, 65536, 78125, 23328, 16807, 4096, 729, 10, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS FORMULA G.f. of column k: Sum_{j>=1} x^j/(j^k*(1 - x^j)) (for rationals Sum_{d|n} 1/d^k). Dirichlet g.f. of column k: zeta(s)*zeta(s+k) (for rationals Sum_{d|n} 1/d^k). A(n,k) = denominator of sigma_k(n)/n^k. EXAMPLE Square array begins:   1,    1,      1,        1,        1,          1,  ...   2,  3/2,    5/4,      9/8,    17/16,      33/32,  ...   2,  4/3,   10/9,    28/27,    82/81,    244/243,  ...   3,  7/4,  21/16,    73/64,  273/256,  1057/1024,  ...   2,  6/5,  26/25,  126/125,  626/625,  3126/3125,  ...   4,    2,  25/18,      7/6,  697/648,    671/648,  ... MATHEMATICA Table[Function[k, Denominator[DivisorSigma[-k, n]]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten Table[Function[k, Denominator[DivisorSigma[k, n]/n^k]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten Table[Function[k, Denominator[SeriesCoefficient[Sum[x^j/(j^k (1 - x^j)), {j, 1, n}], {x, 0, n}]]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten CROSSREFS Columns k=0..24 give A000012, A017666, A017668, A017670, A017672, A017674, A017676, A017678, A017680, A017682, A017684, A017686, A017688, A017690, A017692, A017694, A017696, A017698, A017700, A017702, A017704, A017706, A017708, A017710, A017712. Numerators are in A322263. Cf. A109974, A279394. Sequence in context: A137743 A099239 A167630 * A009998 A113993 A103323 Adjacent sequences:  A322261 A322262 A322263 * A322265 A322266 A322267 KEYWORD nonn,tabl,frac AUTHOR Ilya Gutkovskiy, Dec 01 2018 STATUS approved

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

Last modified May 26 12:33 EDT 2020. Contains 334626 sequences. (Running on oeis4.)