cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A127371 Triangle read by rows: A051731 * A054521, as infinite lower triangular matrices.

Original entry on oeis.org

1, 2, 0, 2, 1, 0, 3, 0, 1, 0, 2, 1, 1, 1, 0, 4, 1, 0, 0, 1, 0, 2, 1, 1, 1, 1, 1, 0, 4, 0, 2, 0, 1, 0, 1, 0, 3, 2, 0, 1, 1, 0, 1, 1, 0, 4, 1, 2, 1, 0, 0, 1, 0, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 6, 1, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0
Offset: 1

Views

Author

Gary W. Adamson, Jan 12 2007

Keywords

Comments

Row sums = n, left column = d(n), (A000005: 1, 2, 2, 3, 2, 4, 2, ...).

Examples

			First few rows of the triangle:
  1;
  2, 0;
  2, 1, 0;
  3, 0, 1, 0;
  2, 1, 1, 1, 0;
  4, 1, 0, 0, 1, 0;
  2, 1, 1, 1, 1, 1, 0;
  4, 0, 2, 0, 1, 0, 1, 0;
  3, 2, 0, 1, 1, 0, 1, 1, 0;
  ...

Crossrefs

Cf. A000005, A051731, A054521.

Formula

Inverse Moebius transform of A054521.

Extensions

Definition clarified, a(56) corrected and more terms from Georg Fischer, May 29 2023

A127372 Triangle read by rows: A127170 * A054521 as infinite lower triangular matrices.

Original entry on oeis.org

1, 3, 0, 3, 1, 0, 6, 0, 1, 0, 3, 1, 1, 1, 0, 9, 2, 0, 0, 1, 0, 3, 1, 1, 1, 1, 1, 0, 10, 0, 3, 0, 1, 0, 1, 0, 6, 3, 0, 1, 1, 0, 1, 1, 0, 9, 2, 3, 2, 0, 0, 1, 0, 1, 0
Offset: 1

Views

Author

Gary W. Adamson, Jan 12 2007

Keywords

Comments

Left column = A007425, (tau_3(n)): 1, 3, 3, 6, 3, 9, ... Row sums = sigma(n), A000203: 1, 3, 4, 7, 6, 12, ...

Examples

			First few rows of the triangle:
   1;
   3, 0;
   3, 1, 0;
   6, 0, 1, 0;
   3, 1, 1, 1, 0;
   9, 2, 0, 0, 1, 0;
   3, 1, 1, 1, 1, 1, 0;
  10, 0, 3, 0, 1, 0, 1, 0;
  ...

Crossrefs

Cf. A127170, A054521, A000203, A007425.

Extensions

Edited by N. J. A. Sloane, Jul 11 2008

A127375 Triangle A126988 * A054521, as infinite lower triangular matrices.

Original entry on oeis.org

1, 3, 0, 4, 1, 0, 7, 0, 1, 0, 6, 1, 1, 1, 0, 12, 2, 0, 0, 1, 0, 8, 1, 1, 1, 1, 1, 0, 15, 0, 3, 0, 1, 0, 1, 0, 13, 4, 0, 1, 1, 0, 1, 1, 0, 18, 2, 3, 2, 0, 0, 1, 0, 1, 0, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 28, 4, 3, 0, 3, 0, 1, 0, 0, 0, 1, 0, 14, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0
Offset: 1

Views

Author

Gary W. Adamson, Jan 12 2007

Keywords

Comments

Left column gives A000203.
Row sums give A018804.

Examples

			First few rows of the triangle are:
1;
3, 0;
4, 1, 0;
7, 0, 1, 0;
6, 1, 1, 1, 0;
12, 2, 0, 0, 1, 0;
8, 1, 1, 1, 1, 1, 0;
...

Crossrefs

Cf. A000203, A018804, A054521, A126988.

Extensions

a(17) = 2 inserted and more terms from Georg Fischer, May 29 2023

A127479 Triangle read by rows: A054522 * A054521 as infinite lower triangular matrices.

Original entry on oeis.org

1, 2, 0, 3, 2, 0, 4, 0, 2, 0, 5, 4, 4, 4, 0, 6, 2, 0, 0, 2, 0, 7, 6, 6, 6, 6, 6, 0, 8, 0, 6, 0, 4, 0, 4, 0, 9, 8, 0, 6, 6, 0, 6, 6, 0, 10, 4, 8, 4, 0, 0, 4, 0, 4, 0
Offset: 1

Views

Author

Gary W. Adamson, Jan 15 2007

Keywords

Comments

Row sums = A029939: (1, 2, 5, 6, 17, 10, 37, ...).

Examples

			First few rows of the triangle:
  1;
  2, 0;
  3, 2, 0;
  4, 0, 2, 0;
  5, 4, 4, 4, 0;
  6, 2, 0, 0, 2, 0;
  7, 6, 6, 6, 6, 6, 0;
  8, 0, 6, 0, 4, 0, 4, 0;
  ...

Crossrefs

Cf. A029939, A054522, A054521.

Extensions

Edited by N. J. A. Sloane, Aug 10 2019

A127506 Triangle read by rows: T(n,k) = A054521(n,k)*A000010(k), 1<=k<=n .

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 1, 2, 2, 0, 1, 0, 0, 0, 4, 0, 1, 1, 2, 2, 4, 2, 0, 1, 0, 2, 0, 4, 0, 6, 0, 1, 1, 0, 2, 4, 0, 6, 4, 0, 1, 0, 2, 0, 0, 0, 6, 0, 6, 0
Offset: 1

Views

Author

Gary W. Adamson, Jan 17 2007

Keywords

Comments

Row sums = A053570.

Examples

			First few rows of the triangle are:
1;
1, 0;
1, 1, 0;
1, 0, 2, 0;
1, 1, 2, 2, 0;
1, 0, 0, 0, 4, 0;
1, 1, 2, 2, 4, 2, 0;
...

Crossrefs

Cf. A054521, A000010, A053570.

Formula

A054521 * M, as infinite lower triangular matrices; M = phi(n) in the main diagonal and the rest zeros.

Extensions

Edited by R. J. Mathar, Jan 09 2008

A128306 Triangle read by rows: A054521 * A007318 as infinite lower triangular matrices.

Original entry on oeis.org

1, 1, 0, 2, 1, 0, 2, 2, 1, 0, 4, 6, 4, 1, 0, 2, 4, 6, 4, 1, 0, 6, 15, 20, 15, 6, 1, 0, 4, 12, 22, 24, 16, 6, 1, 0, 6, 21, 45, 60, 51, 27, 8, 1, 0, 4, 16, 44, 76, 85, 62, 29, 8, 1, 0, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 0, 4, 20, 66, 144, 226, 258, 211, 120, 45, 10, 1, 0
Offset: 1

Views

Author

Gary W. Adamson, Feb 25 2007

Keywords

Comments

Left border = phi(n), A000010: (1, 1, 2, 2, 4, 2, 6, ...). Row sums = A054432: (1, 1, 3, 5, 15, 17, 63, ...).

Examples

			First few rows of the triangle:
  1;
  1,  0;
  2,  1,  0;
  2,  2,  1,  0;
  4,  6,  4,  1,  0;
  2,  4,  6,  4,  1,  0;
  6, 15, 20, 15,  6,  1,  0;
  ...

Crossrefs

Cf. A000010, A007318, A054432, A054521.

Extensions

Definition amended and terms starting at a(56) corrected by Georg Fischer, May 29 2023

A128431 Triangle read by rows: A054521 * A128407.

Original entry on oeis.org

1, 1, 0, 1, -1, 0, 1, 0, -1, 0, 1, -1, -1, 0, 0, 1, 0, 0, 0, -1, 0, 1, -1, -1, 0, -1, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 1, -1, 0, 0, -1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0
Offset: 1

Views

Author

Gary W. Adamson, Mar 03 2007

Keywords

Comments

Row sums = A112399: (1, 1, 0, 0, -1, 0, -1, -2, -2, -1, ...).

Examples

			First few rows of the triangle:
  1;
  1,  0;
  1, -1,  0;
  1,  0, -1,  0;
  1, -1, -1,  0,  0;
  1,  0,  0,  0, -1,  0;
  1, -1, -1,  0, -1,  1,  0;

Crossrefs

Cf. A054521, A128407, A112399, A008683.

Formula

A054521 * A128407 as infinite lower triangular matrices.

A128432 Triangle read by rows: A128407 * A054521.

Original entry on oeis.org

1, -1, 0, -1, -1, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0
Offset: 1

Views

Author

Gary W. Adamson, Mar 03 2007

Keywords

Comments

Row sums = A023900: (1, -1, -2, 0, -4, 2, -6, ...) Left border = mu(n), A008683.

Examples

			First few rows of the triangle:
   1;
  -1,  0;
  -1, -1,  0;
   0,  0,  0,  0;
  -1, -1, -1, -1,  0;
   1,  0,  0,  0,  1,  0;
  -1, -1, -1, -1, -1, -1,  0;
   0,  0,  0,  0,  0,  0,  0,  0;
  ...

Crossrefs

Cf. A128407, A054521, A008683, A023900.

Formula

A128407 * A054521 as infinite lower triangular matrices.

A128584 A054521 * A128064 (unsigned).

Original entry on oeis.org

1, 1, 0, 0, 2, 0, 1, -2, 3, 0, 0, 0, 0, 4, 0, 1, 0, 0, -4, 5, 0, 0, 0, 0, 0, 0, 6, 0, 1, -2, 3, -4, 5, -6, 7, 0, 0, 2, -3, 0, 5, -6, 0, 8, 0, 1, -2, 3, 0, 0, -6, 7, -8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 1, 0, 0, -4, 5, -6, 7, 0, 0, -10, 11, 0
Offset: 1

Views

Author

Gary W. Adamson, Mar 11 2007

Keywords

Comments

Row sums = phi(n), A000010: (1, 1, 2, 2, 4, 2, 6, 4, 6, 4, ...).

Examples

			First few rows of the triangle:
  1;
  1,  0;
  0,  2,  0;
  1, -2,  3,  0;
  0,  0,  0,  4,  0;
  1,  0,  0, -4,  5,  0;
  ...

Crossrefs

Cf. A054521, A128064, A000010.

Formula

A054521 * A128064 (unsigned) as infinite lower triangular matrices.

Extensions

a(28) = 0 inserted and more terms from Georg Fischer, May 29 2023

A129239 Triangle read by rows: A054521 * A129234 as infinite lower triangular matrices.

Original entry on oeis.org

1, 1, 0, 3, 2, 0, 4, 0, 3, 0, 10, 5, 3, 4, 0, 6, 0, 0, 0, 5, 0, 21, 9, 7, 4, 5, 6, 0, 16, 0, 3, 0, 5, 0, 7, 0, 27, 10, 0, 9, 5, 0, 7, 8, 0, 20, 0, 8, 0, 0, 0, 7, 0, 9, 0, 55, 20, 12, 9, 11, 6, 7, 8, 9, 10, 0, 24, 0, 0, 0, 5, 0, 7, 0, 0, 0, 11, 0, 78, 27, 18, 15, 11, 13, 7, 8, 9, 10, 11, 12, 0
Offset: 1

Views

Author

Gary W. Adamson, Apr 05 2007

Keywords

Comments

Left column = A023896: (1, 1, 3, 4, 10, 6, 21, ...).

Examples

			First few rows of the triangle:
   1;
   1, 0;
   3, 2, 0;
   4, 0, 3, 0;
  10, 5, 3, 4, 0;
   6, 0, 0, 0, 5, 0;
  21, 9, 7, 4, 5, 6, 0;
  16, 0, 3, 0, 5, 0, 7, 0;
  ...

Crossrefs

Cf. A023896, A054521, A129234.

Extensions

a(21) = 0 inserted and more terms from Georg Fischer, May 29 2023
Previous Showing 11-20 of 59 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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