A127172 Cube of A051731.

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

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