A323226 T(n, k) = p(n) - (p(k) - t(k-1)) with t(n) = A000005(|n|) for n != 0 and t(0) = 0, p(n) = A000010(n) for n > 0 and p(0) = 0, for n >= 0 and 0 <= k <= n, triangle read by rows.

1, 2, 0, 2, 0, 1, 3, 1, 2, 2, 3, 1, 2, 2, 2, 5, 3, 4, 4, 4, 3, 3, 1, 2, 2, 2, 1, 2, 7, 5, 6, 6, 6, 5, 6, 4, 5, 3, 4, 4, 4, 3, 4, 2, 2, 7, 5, 6, 6, 6, 5, 6, 4, 4, 4, 5, 3, 4, 4, 4, 3, 4, 2, 2, 2, 3, 11, 9, 10, 10, 10, 9, 10, 8, 8, 8, 9, 4, 5, 3, 4, 4, 4, 3, 4, 2, 2, 2, 3, -2, 2

Offset

0,2

Links

Table of n, a(n) for n=0..90.

Peter Luschny, Plot of the function.

Example

Triangle starts:
[0]  1
[1]  2, 0
[2]  2, 0, 1
[3]  3, 1, 2, 2
[4]  3, 1, 2, 2, 2
[5]  5, 3, 4, 4, 4, 3
[6]  3, 1, 2, 2, 2, 1, 2
[7]  7, 5, 6, 6, 6, 5, 6, 4
[8]  5, 3, 4, 4, 4, 3, 4, 2, 2
[9]  7, 5, 6, 6, 6, 5, 6, 4, 4, 4

Maple

with(numtheory):
T := (n, k) -> phi(n) - (phi(k) - tau(k-1)):
seq(seq(T(n, k), k=0..n), n=0..12);

Mathematica

phi[n_] := EulerPhi[n]; tau[n_] := If[n == 0, 0, DivisorSigma[0, n]];
T[n_, k_] := phi[n] - (phi[k] - tau[k - 1]);
Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten

Crossrefs

Cf. A000005, A000010.

Sequence in context: A022879 A340524 A064984 * A307197 A328949 A038555

Adjacent sequences: A323223 A323224 A323225 * A323227 A323228 A323229

Keyword

sign,tabl,easy

Author

Peter Luschny, Feb 19 2019

Status

approved