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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:

   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,uned

AUTHOR

Gary W. Adamson, Jan 06 2007

STATUS

approved

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Last modified July 3 18:06 EDT 2022. Contains 355055 sequences. (Running on oeis4.)