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 1-7 of 7 results.

A339701 Dirichlet g.f.: Product_{k>=2} (1 - k^(-s))^2.

Original entry on oeis.org

1, -2, -2, -1, -2, 2, -2, 2, -1, 2, -2, 4, -2, 2, 2, 1, -2, 4, -2, 4, 2, 2, -2, 0, -1, 2, 2, 4, -2, 2, -2, 2, 2, 2, 2, 0, -2, 2, 2, 0, -2, 2, -2, 4, 4, 2, -2, -2, -1, 4, 2, 4, -2, 0, 2, 0, 2, 2, -2, -4, -2, 2, 4, -2, 2, 2, -2, 4, 2, 2, -2, -4, -2, 2, 4, 4, 2, 2, -2, -2
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 13 2020

Keywords

Crossrefs

Cf. A002107, A114592, A301830, A339702, A339703, A339704, A339705, A339706, A339707.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A301830(n/d) * a(d).
a(n) = Sum_{d|n} A114592(n/d) * A114592(d).
a(p^k) = A002107(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.

A339703 Dirichlet g.f.: Product_{k>=2} (1 - k^(-s))^4.

Original entry on oeis.org

1, -4, -4, 2, -4, 12, -4, 8, 2, 12, -4, 4, -4, 12, 12, -5, -4, 4, -4, 4, 12, 12, -4, -28, 2, 12, 8, 4, -4, -20, -4, -4, 12, 12, 12, -26, -4, 12, 12, -28, -4, -20, -4, 4, 4, 12, -4, -8, 2, 4, 12, 4, -4, -28, 12, -28, 12, 12, -4, -44, -4, 12, 4, -10, 12, -20, -4, 4, 12, -20
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 13 2020

Keywords

Crossrefs

Cf. A000727, A114592, A339319, A339701, A339702, A339704, A339705, A339706, A339707.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A339319(n/d) * a(d).
a(p^k) = A000727(k) for prime p.

A339704 Dirichlet g.f.: Product_{k>=2} (1 - k^(-s))^5.

Original entry on oeis.org

1, -5, -5, 5, -5, 20, -5, 10, 5, 20, -5, -5, -5, 20, 20, -15, -5, -5, -5, -5, 20, 20, -5, -55, 5, 20, 10, -5, -5, -55, -5, -6, 20, 20, 20, -45, -5, 20, 20, -55, -5, -55, -5, -5, -5, 20, -5, 20, 5, -5, 20, -5, -5, -55, 20, -55, 20, 20, -5, -55, -5, 20, -5, -5, 20, -55, -5, -5, 20, -55
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 13 2020

Keywords

Crossrefs

Cf. A000728, A114592, A339320, A339701, A339702, A339703, A339705, A339706, A339707.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A339320(n/d) * a(d).
a(p^k) = A000728(k) for prime p.

A339705 Dirichlet g.f.: Product_{k>=2} (1 - k^(-s))^6.

Original entry on oeis.org

1, -6, -6, 9, -6, 30, -6, 10, 9, 30, -6, -24, -6, 30, 30, -30, -6, -24, -6, -24, 30, 30, -6, -84, 9, 30, 10, -24, -6, -114, -6, 0, 30, 30, 30, -54, -6, 30, 30, -84, -6, -114, -6, -24, -24, 30, -6, 96, 9, -24, 30, -24, -6, -84, 30, -84, 30, 30, -6, -24, -6, 30, -24, 11, 30
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 13 2020

Keywords

Crossrefs

Cf. A000729, A114592, A339321, A339701, A339702, A339703, A339704, A339706, A339707.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A339321(n/d) * a(d).
a(p^k) = A000729(k) for prime p.

A339707 Dirichlet g.f.: Product_{k>=2} (1 - k^(-s))^8.

Original entry on oeis.org

1, -8, -8, 20, -8, 56, -8, 0, 20, 56, -8, -104, -8, 56, 56, -70, -8, -104, -8, -104, 56, 56, -8, -104, 20, 56, 0, -104, -8, -328, -8, 64, 56, 56, 56, 36, -8, 56, 56, -104, -8, -328, -8, -104, -104, 56, -8, 456, 20, -104, 56, -104, -8, -104, 56, -104, 56, 56, -8, 344, -8, 56, -104, 56, 56
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 13 2020

Keywords

Crossrefs

Cf. A000731, A114592, A339323, A339701, A339702, A339703, A339704, A339705, A339706.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A339323(n/d) * a(d).
a(p^k) = A000731(k) for prime p.

A339716 Dirichlet g.f.: Product_{k>=2} (1 - k^(-s))^9.

Original entry on oeis.org

1, -9, -9, 27, -9, 72, -9, -12, 27, 72, -9, -171, -9, 72, 72, -90, -9, -171, -9, -171, 72, 72, -9, -63, 27, 72, -12, -171, -9, -495, -9, 135, 72, 72, 72, 189, -9, 72, 72, -63, -9, -495, -9, -171, -171, 72, -9, 747, 27, -171, 72, -171, -9, -63, 72, -63, 72, 72, -9, 801
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 14 2020

Keywords

Crossrefs

Cf. A010817, A114592, A339324, A339701, A339702, A339703, A339704, A339705, A339706, A339707.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A339324(n/d) * a(d).
a(p^k) = A010817(k) for prime p.
Showing 1-7 of 7 results.

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