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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
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 (list; table; graph; refs; listen; history; text; internal format)
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: A265247 A022879 A064984 * A307197 A038555 A138108

Adjacent sequences:  A323223 A323224 A323225 * A323227 A323228 A323229

KEYWORD

sign,tabl,easy

AUTHOR

Peter Luschny, Feb 19 2019

STATUS

approved

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Last modified October 22 07:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)