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A327029 T(n, k) = Sum_{d|n} phi(d) * A008284(n/d, k) for n >= 1, T(0, 0) = 1. Triangle read by rows for 0 <= k <= n. 8
1, 0, 1, 0, 2, 1, 0, 3, 1, 1, 0, 4, 3, 1, 1, 0, 5, 2, 2, 1, 1, 0, 6, 6, 4, 2, 1, 1, 0, 7, 3, 4, 3, 2, 1, 1, 0, 8, 8, 6, 6, 3, 2, 1, 1, 0, 9, 6, 9, 6, 5, 3, 2, 1, 1, 0, 10, 11, 10, 10, 8, 5, 3, 2, 1, 1, 0, 11, 5, 10, 11, 10, 7, 5, 3, 2, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..77.

EXAMPLE

Triangle starts:

[0] [1]

[1] [0, 1]

[2] [0, 2, 1]

[3] [0, 3, 1, 1]

[4] [0, 4, 3, 1, 1]

[5] [0, 5, 2, 2, 1, 1]

[6] [0, 6, 6, 4, 2, 1, 1]

[7] [0, 7, 3, 4, 3, 2, 1, 1]

[8] [0, 8, 8, 6, 6, 3, 2, 1, 1]

[9] [0, 9, 6, 9, 6, 5, 3, 2, 1, 1]

PROG

(SageMath)

def DivisorTriangle(f, T, Len, w = None):

    D = [[1]]

    for n in (1..Len-1):

        r = lambda k: [f(d)*T(n//d, k) for d in divisors(n)]

        L = [sum(r(k)) for k in (0..n)]

        if w != None: L = map(lambda v: v * w(n), L)

        D.append(L)

    return D

DivisorTriangle(euler_phi, A008284, 10)

CROSSREFS

Cf. A008284, A000010, A078392 (row sums), A282750.

Sequence in context: A285037 A264422 A176808 * A167192 A262114 A320780

Adjacent sequences:  A327026 A327027 A327028 * A327030 A327031 A327032

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Aug 24 2019

STATUS

approved

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)