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 A258651 A(n,k) = n^(k) = k-th arithmetic derivative of n; square array A(n,k), n>=0, k>=0, read by antidiagonals. 16
 0, 0, 1, 0, 0, 2, 0, 0, 1, 3, 0, 0, 0, 1, 4, 0, 0, 0, 0, 4, 5, 0, 0, 0, 0, 4, 1, 6, 0, 0, 0, 0, 4, 0, 5, 7, 0, 0, 0, 0, 4, 0, 1, 1, 8, 0, 0, 0, 0, 4, 0, 0, 0, 12, 9, 0, 0, 0, 0, 4, 0, 0, 0, 16, 6, 10, 0, 0, 0, 0, 4, 0, 0, 0, 32, 5, 7, 11, 0, 0, 0, 0, 4, 0, 0, 0, 80, 1, 1, 1, 12 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Alois P. Heinz, Antidiagonals n = 0..100 J. Kovič, The Arithmetic Derivative and Antiderivative, Journal of Integer Sequences 15 (2012), Article 12.3.8 Wikipedia, Arithmetic derivative FORMULA A(n,k) = A003415^k(n). EXAMPLE Square array A(n,k) begins:   0,  0,  0,  0,  0,   0,   0,   0,    0,    0, ...   1,  0,  0,  0,  0,   0,   0,   0,    0,    0, ...   2,  1,  0,  0,  0,   0,   0,   0,    0,    0, ...   3,  1,  0,  0,  0,   0,   0,   0,    0,    0, ...   4,  4,  4,  4,  4,   4,   4,   4,    4,    4, ...   5,  1,  0,  0,  0,   0,   0,   0,    0,    0, ...   6,  5,  1,  0,  0,   0,   0,   0,    0,    0, ...   7,  1,  0,  0,  0,   0,   0,   0,    0,    0, ...   8, 12, 16, 32, 80, 176, 368, 752, 1520, 3424, ...   9,  6,  5,  1,  0,   0,   0,   0,    0,    0, ... MAPLE d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]): A:= proc(n, k) option remember; `if`(k=0, n, d(A(n, k-1))) end: seq(seq(A(n, h-n), n=0..h), h=0..14); MATHEMATICA d[n_] := n*Sum[i[[2]]/i[[1]], {i, FactorInteger[n]}]; d[0] = d[1] = 0; A[n_, k_] := A[n, k] = If[k == 0, n, d[A[n, k-1]]]; Table[A[n, h-n], {h, 0, 14}, {n, 0, h}] // Flatten (* Jean-François Alcover, Apr 27 2017, translated from Maple *) CROSSREFS Columns k=0-10 give: A001477, A003415, A068346, A099306, A258644, A258645, A258646, A258647, A258648, A258649, A258650. Rows n=0,1,4,8 give: A000004, A000007, A010709, A129150. Main diagonal gives A185232. Antidiagonal sums give A258652. Sequence in context: A325201 A260019 A153036 * A258850 A182114 A122950 Adjacent sequences:  A258648 A258649 A258650 * A258652 A258653 A258654 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Jun 06 2015 STATUS approved

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Last modified December 16 04:05 EST 2019. Contains 330013 sequences. (Running on oeis4.)