OFFSET
1,3
LINKS
Seiichi Manyama, Antidiagonals n = 1..140, flattened
FORMULA
G.f. of column k: (1/(1 - x)) * Sum_{i>=1} phi(i) * ( Sum_{j=1..k} A008292(k, j) * x^(i*j) )/(1 - x^i)^k.
T(n,k) = Sum_{j=1..n} phi(j) * floor(n/j)^k.
EXAMPLE
G.f. of column 3: (1/(1 - x)) * Sum_{i>=1} phi(i) * (x^i + 4*x^(2*i) + x^(3*i))/(1 - x^i)^3.
Square array begins:
1, 1, 1, 1, 1, 1, ...
3, 5, 9, 17, 33, 65, ...
6, 12, 30, 84, 246, 732, ...
10, 24, 76, 276, 1060, 4164, ...
15, 37, 141, 649, 3165, 15697, ...
21, 61, 267, 1417, 8091, 47521, ...
MATHEMATICA
T[n_, k_] := Sum[EulerPhi[j] * Quotient[n, j]^k, {j, 1, n}]; Table[T[k, n - k + 1], {n, 1, 11}, {k, 1, n}] // Flatten (* Amiram Eldar, May 22 2021 *)
PROG
(PARI) T(n, k) = sum(j=1, n, eulerphi(j)*(n\j)^k);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, May 22 2021
STATUS
approved