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.

Showing 1-9 of 9 results.

A339319 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^4.

Original entry on oeis.org

1, 4, 4, 14, 4, 20, 4, 40, 14, 20, 4, 76, 4, 20, 20, 105, 4, 76, 4, 76, 20, 20, 4, 236, 14, 20, 40, 76, 4, 116, 4, 252, 20, 20, 20, 306, 4, 20, 20, 236, 4, 116, 4, 76, 76, 20, 4, 656, 14, 76, 20, 76, 4, 236, 20, 236, 20, 20, 4, 476, 4, 20, 76, 574, 20, 116, 4, 76, 20, 116
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 30 2020

Keywords

Comments

Number of factorizations of n into factors (greater than 1) of 4 kinds.

Crossrefs

Cf. A001055, A023003, A301830, A339318, A339320, A339321, A339322, A339323, A339324.

Formula

a(p^k) = A023003(k) for prime p.

A339320 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^5.

Original entry on oeis.org

1, 5, 5, 20, 5, 30, 5, 65, 20, 30, 5, 130, 5, 30, 30, 190, 5, 130, 5, 130, 30, 30, 5, 455, 20, 30, 65, 130, 5, 205, 5, 506, 30, 30, 30, 595, 5, 30, 30, 455, 5, 205, 5, 130, 130, 30, 5, 1405, 20, 130, 30, 130, 5, 455, 30, 455, 30, 30, 5, 955, 5, 30, 130, 1265, 30, 205, 5, 130
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 30 2020

Keywords

Comments

Number of factorizations of n into factors (greater than 1) of 5 kinds.

Crossrefs

Cf. A001055, A023004, A301830, A339318, A339319, A339321, A339322, A339323, A339324.

Formula

a(p^k) = A023004(k) for prime p.

A339321 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^6.

Original entry on oeis.org

1, 6, 6, 27, 6, 42, 6, 98, 27, 42, 6, 204, 6, 42, 42, 315, 6, 204, 6, 204, 42, 42, 6, 792, 27, 42, 98, 204, 6, 330, 6, 918, 42, 42, 42, 1044, 6, 42, 42, 792, 6, 330, 6, 204, 204, 42, 6, 2682, 27, 204, 42, 204, 6, 792, 42, 792, 42, 42, 6, 1716, 6, 42, 204, 2492, 42, 330
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 30 2020

Keywords

Comments

Number of factorizations of n into factors (greater than 1) of 6 kinds.

Crossrefs

Cf. A001055, A023005, A301830, A339318, A339319, A339320, A339322, A339323, A339324.

Formula

a(p^k) = A023005(k) for prime p.

A339322 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^7.

Original entry on oeis.org

1, 7, 7, 35, 7, 56, 7, 140, 35, 56, 7, 301, 7, 56, 56, 490, 7, 301, 7, 301, 56, 56, 7, 1281, 35, 56, 140, 301, 7, 497, 7, 1547, 56, 56, 56, 1701, 7, 56, 56, 1281, 7, 497, 7, 301, 301, 56, 7, 4711, 35, 301, 56, 301, 7, 1281, 56, 1281, 56, 56, 7, 2849, 7, 56, 301, 4522
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 30 2020

Keywords

Comments

Number of factorizations of n into factors (greater than 1) of 7 kinds.

Crossrefs

Cf. A001055, A023006, A301830, A339318, A339319, A339320, A339321, A339323, A339324.

Formula

a(p^k) = A023006(k) for prime p.

A339323 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^8.

Original entry on oeis.org

1, 8, 8, 44, 8, 72, 8, 192, 44, 72, 8, 424, 8, 72, 72, 726, 8, 424, 8, 424, 72, 72, 8, 1960, 44, 72, 192, 424, 8, 712, 8, 2464, 72, 72, 72, 2620, 8, 72, 72, 1960, 8, 712, 8, 424, 424, 72, 8, 7768, 44, 424, 72, 424, 8, 1960, 72, 1960, 72, 72, 8, 4456, 8, 72, 424
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 30 2020

Keywords

Comments

Number of factorizations of n into factors (greater than 1) of 8 kinds.

Crossrefs

Cf. A001055, A023007, A301830, A339318, A339319, A339320, A339321, A339322, A339324.

Formula

a(p^k) = A023007(k) for prime p.

A339324 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^9.

Original entry on oeis.org

1, 9, 9, 54, 9, 90, 9, 255, 54, 90, 9, 576, 9, 90, 90, 1035, 9, 576, 9, 576, 90, 90, 9, 2871, 54, 90, 255, 576, 9, 981, 9, 3753, 90, 90, 90, 3861, 9, 90, 90, 2871, 9, 981, 9, 576, 576, 90, 9, 12186, 54, 576, 90, 576, 9, 2871, 90, 2871, 90, 90, 9, 6651, 9, 90, 576
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 30 2020

Keywords

Comments

Number of factorizations of n into factors (greater than 1) of 9 kinds.

Crossrefs

Cf. A001055, A023008, A301830, A339318, A339319, A339320, A339321, A339322, A339323.

Formula

a(p^k) = A023008(k) for prime p.

A339335 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^3.

Original entry on oeis.org

1, 3, 3, 6, 3, 12, 3, 13, 6, 12, 3, 30, 3, 12, 12, 24, 3, 30, 3, 30, 12, 12, 3, 69, 6, 12, 13, 30, 3, 57, 3, 42, 12, 12, 12, 87, 3, 12, 12, 69, 3, 57, 3, 30, 30, 12, 3, 141, 6, 30, 12, 30, 3, 69, 12, 69, 12, 12, 3, 165, 3, 12, 30, 73, 12, 57, 3, 30, 12, 57, 3, 216, 3, 12, 30
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 30 2020

Keywords

Crossrefs

Cf. A022568, A045778, A328706, A339318, A339336, A339337, A339338, A339339, A339340, A339341.

Formula

a(p^k) = A022568(k) for prime p.

A339702 Dirichlet g.f.: Product_{k>=2} (1 - k^(-s))^3.

Original entry on oeis.org

1, -3, -3, 0, -3, 6, -3, 5, 0, 6, -3, 6, -3, 6, 6, 0, -3, 6, -3, 6, 6, 6, -3, -9, 0, 6, 5, 6, -3, -3, -3, 0, 6, 6, 6, -9, -3, 6, 6, -9, -3, -3, -3, 6, 6, 6, -3, -9, 0, 6, 6, 6, -3, -9, 6, -9, 6, 6, -3, -21, -3, 6, 6, -7, 6, -3, -3, 6, 6, -3, -3, -12, -3, 6, 6, 6, 6, -3, -3, -9
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 13 2020

Keywords

Crossrefs

Cf. A010816, A114592, A339318, A339701, A339703, A339704, A339705, A339706, A339707.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A339318(n/d) * a(d).
a(p^k) = A010816(k) for prime p.

A349922 Dirichlet g.f.: Product_{k>=2} 1 / (1 - 3 * k^(-s)).

Original entry on oeis.org

1, 3, 3, 12, 3, 12, 3, 39, 12, 12, 3, 48, 3, 12, 12, 129, 3, 48, 3, 48, 12, 12, 3, 165, 12, 12, 39, 48, 3, 57, 3, 399, 12, 12, 12, 201, 3, 12, 12, 165, 3, 57, 3, 48, 48, 12, 3, 552, 12, 48, 12, 48, 3, 165, 12, 165, 12, 12, 3, 237, 3, 12, 48, 1245, 12, 57, 3, 48, 12, 57
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 05 2021

Keywords

Crossrefs

Cf. A001055, A165824, A242587, A339318, A349921.
Showing 1-9 of 9 results.

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