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 A185651 A(n,k) = Sum_{d|n} phi(d)*k^(n/d); square array A(n,k), n>=0, k>=0, read by antidiagonals. 23
 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 6, 3, 0, 0, 4, 12, 12, 4, 0, 0, 5, 20, 33, 24, 5, 0, 0, 6, 30, 72, 96, 40, 6, 0, 0, 7, 42, 135, 280, 255, 84, 7, 0, 0, 8, 56, 228, 660, 1040, 780, 140, 8, 0, 0, 9, 72, 357, 1344, 3145, 4200, 2205, 288, 9, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened FORMULA A(n,k) = Sum_{d|n} phi(d)*k^(n/d). A(n,k) = Sum_{i=0..min(n,k)} C(k,i) * i! * A258170(n,i). - Alois P. Heinz, May 22 2015 G.f. for column k: Sum_{n>=1} phi(n)*k*x^n/(1-k*x^n) for k >= 0. - Petros Hadjicostas, Nov 06 2017 EXAMPLE Square array A(n,k) begins:   0, 0,  0,   0,    0,     0,     0, ...   0, 1,  2,   3,    4,     5,     6, ...   0, 2,  6,  12,   20,    30,    42, ...   0, 3, 12,  33,   72,   135,   228, ...   0, 4, 24,  96,  280,   660,  1344, ...   0, 5, 40, 255, 1040,  3145,  7800, ...   0, 6, 84, 780, 4200, 15810, 46956, ... MAPLE with(numtheory): A:= (n, k)-> add(phi(d)*k^(n/d), d=divisors(n)): seq(seq(A(n, d-n), n=0..d), d=0..12); MATHEMATICA a[_, 0] = a[0, _] = 0; a[n_, k_] := Sum[EulerPhi[d]*k^(n/d), {d, Divisors[n]}]; Table[a[n - k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Dec 06 2013 *) CROSSREFS Columns k=0..10 give A000004, A001477, A053635, A054610, A054611, A054612, A054613, A054614, A054615, A054616, A054617. Rows n=0..10 give A000004, A001477, A002378, A054602, A054603, A054604, A054605, A054606, A054607, A054608, A054609. Main diagonal gives A228640. Cf. A000010, A258170. Sequence in context: A014473 A226545 A271917 * A265080 A228275 A228250 Adjacent sequences:  A185648 A185649 A185650 * A185652 A185653 A185654 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Aug 29 2013 STATUS approved

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Last modified August 25 14:35 EDT 2019. Contains 326324 sequences. (Running on oeis4.)