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A127172 Cube of A051731. 4
1, 3, 1, 3, 0, 1, 6, 3, 0, 1, 3, 0, 0, 0, 1, 9, 3, 3, 0, 0, 1, 3, 0, 0, 0, 0, 0, 1, 10, 6, 0, 3, 0, 0, 0, 1, 6, 0, 3, 0, 0, 0, 0, 0, 1, 9, 3, 0, 0, 0, 3, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Nonzero terms in every column = A007425: (1, 3, 3, 6, 3, 9, 3,...). Row sums = A007426: (1, 4, 4, 20, 4, 16,...) A127172 * mu(n) = d(n); or A127172 * A008683 = A000005 A127172 * d(n) = tau_5(n); or A127172 * A000005 = A061200. A127172 * phi(n) = A007429: (1, 4, 5, 11, 7, 20,...); or: A127172 * A000010 = A007429. Note that A051731 * d(n) = row sums of A127172; or A051731 * A000005 = A007425. Also, A126988 * mu(n) = phi(n); or A126988 * A008683 = A000010. A126988 * phi(n) = A018804: (1, 3, 5, 8, 9, 15,...); = A127170 * mu(n).

LINKS

Table of n, a(n) for n=1..56.

FORMULA

Cube of A051731 A007425: (1, 3, 3, 6, 3, 9, 3,...) in every column k, interspersed with (k-1) zeros.

EXAMPLE

First few rows of the triangle are:

1;

3, 1;

3, 0, 1;

6, 3, 0, 1;

3, 0, 0, 0, 1;

9, 3, 3, 0, 0, 1;

3, 0, 0, 0, 0, 0, 1;

10, 6, 0, 3, 0, 0, 0, 1;

6, 0, 3, 0, 0, 0, 0, 0, 1;

9, 3, 0, 0, 3, 0, 0, 0, 0, 1;

...

CROSSREFS

Cf. A000005, A007425, A127170, A051731, A007429, A000010, A126988, A018804.

Sequence in context: A136157 A266260 A143353 * A011087 A180021 A091422

Adjacent sequences:  A127169 A127170 A127171 * A127173 A127174 A127175

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jan 06 2007

STATUS

approved

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Last modified April 10 11:35 EDT 2021. Contains 342845 sequences. (Running on oeis4.)