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 1-8 of 8 results.

A339717 Dirichlet g.f.: Product_{k>=2} 1 / (1 + k^(-s))^2.

Original entry on oeis.org

1, -2, -2, 1, -2, 2, -2, -2, 1, 2, -2, 0, -2, 2, 2, 4, -2, 0, -2, 0, 2, 2, -2, 4, 1, 2, -2, 0, -2, 2, -2, -4, 2, 2, 2, 2, -2, 2, 2, 4, -2, 2, -2, 0, 0, 2, -2, -4, 1, 0, 2, 0, -2, 4, 2, 4, 2, 2, -2, 0, -2, 2, 0, 5, 2, 2, -2, 0, 2, 2, -2, -4, -2, 2, 0, 0, 2, 2, -2, -4
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 14 2020

Keywords

Crossrefs

Cf. A022597, A316441, A328706, A339718, A339719, A339720, A339721, A339722.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A328706(n/d) * a(d).
a(n) = Sum_{d|n} A316441(n/d) * A316441(d).
a(p^k) = A022597(k) for prime p.

A339719 Dirichlet g.f.: Product_{k>=2} 1 / (1 + k^(-s))^4.

Original entry on oeis.org

1, -4, -4, 6, -4, 12, -4, -8, 6, 12, -4, -12, -4, 12, 12, 17, -4, -12, -4, -12, 12, 12, -4, 20, 6, 12, -8, -12, -4, -20, -4, -28, 12, 12, 12, 10, -4, 12, 12, 20, -4, -20, -4, -12, -12, 12, -4, -48, 6, -12, 12, -12, -4, 20, 12, 20, 12, 12, -4, 4, -4, 12, -12, 38, 12, -20, -4, -12, 12, -20
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 14 2020

Keywords

Crossrefs

Cf. A022599, A316441, A339336, A339717, A339718, A339720, A339721, A339722.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A339336(n/d) * a(d).
a(p^k) = A022599(k) for prime p.

A339720 Dirichlet g.f.: Product_{k>=2} 1 / (1 + k^(-s))^5.

Original entry on oeis.org

1, -5, -5, 10, -5, 20, -5, -15, 10, 20, -5, -30, -5, 20, 20, 30, -5, -30, -5, -30, 20, 20, -5, 45, 10, 20, -15, -30, -5, -55, -5, -56, 20, 20, 20, 35, -5, 20, 20, 45, -5, -55, -5, -30, -30, 20, -5, -105, 10, -30, 20, -30, -5, 45, 20, 45, 20, 20, -5, 45, -5, 20, -30, 85, 20
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 14 2020

Keywords

Crossrefs

Cf. A022600, A316441, A339337, A339717, A339718, A339719, A339721, A339722.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A339337(n/d) * a(d).
a(p^k) = A022600(k) for prime p.

A339721 Dirichlet g.f.: Product_{k>=2} 1 / (1 + k^(-s))^6.

Original entry on oeis.org

1, -6, -6, 15, -6, 30, -6, -26, 15, 30, -6, -60, -6, 30, 30, 51, -6, -60, -6, -60, 30, 30, -6, 96, 15, 30, -26, -60, -6, -114, -6, -102, 30, 30, 30, 96, -6, 30, 30, 96, -6, -114, -6, -60, -60, 30, -6, -210, 15, -60, 30, -60, -6, 96, 30, 96, 30, 30, -6, 156, -6, 30, -60, 172, 30
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 14 2020

Keywords

Crossrefs

Cf. A022601, A316441, A339338, A339717, A339718, A339719, A339720, A339722.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A339338(n/d) * a(d).
a(p^k) = A022601(k) for prime p.

A339722 Dirichlet g.f.: Product_{k>=2} 1 / (1 + k^(-s))^7.

Original entry on oeis.org

1, -7, -7, 21, -7, 42, -7, -42, 21, 42, -7, -105, -7, 42, 42, 84, -7, -105, -7, -105, 42, 42, -7, 189, 21, 42, -42, -105, -7, -203, -7, -175, 42, 42, 42, 217, -7, 42, 42, 189, -7, -203, -7, -105, -105, 42, -7, -399, 21, -105, 42, -105, -7, 189, 42, 189, 42, 42, -7, 385
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 14 2020

Keywords

Crossrefs

Cf. A022602, A316441, A339339, A339717, A339718, A339719, A339720, A339721.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A339339(n/d) * a(d).
a(p^k) = A022602(k) for prime p.

A339734 Dirichlet g.f.: Product_{k>=2} 1 / (1 + k^(-s))^8.

Original entry on oeis.org

1, -8, -8, 28, -8, 56, -8, -64, 28, 56, -8, -168, -8, 56, 56, 134, -8, -168, -8, -168, 56, 56, -8, 344, 28, 56, -64, -168, -8, -328, -8, -288, 56, 56, 56, 428, -8, 56, 56, 344, -8, -328, -8, -168, -168, 56, -8, -728, 28, -168, 56, -168, -8, 344, 56, 344, 56, 56, -8, 792
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 14 2020

Keywords

Crossrefs

Cf. A007259, A316441, A339340, A339717, A339718, A339719, A339720, A339721, A339722, A339735.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A339340(n/d) * a(d).
a(p^k) = A007259(k) for prime p.

A339735 Dirichlet g.f.: Product_{k>=2} 1 / (1 + k^(-s))^9.

Original entry on oeis.org

1, -9, -9, 36, -9, 72, -9, -93, 36, 72, -9, -252, -9, 72, 72, 207, -9, -252, -9, -252, 72, 72, -9, 585, 36, 72, -93, -252, -9, -495, -9, -459, 72, 72, 72, 765, -9, 72, 72, 585, -9, -495, -9, -252, -252, 72, -9, -1278, 36, -252, 72, -252, -9, 585, 72, 585, 72, 72, -9, 1449
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 14 2020

Keywords

Crossrefs

Cf. A022604, A316441, A339341, A339717, A339718, A339719, A339720, A339721, A339722, A339734.

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A339341(n/d) * a(d).
a(p^k) = A022604(k) for prime p.

A351024 Dirichlet g.f.: Product_{k>=2} 1 / (1 + 3 * k^(-s)).

Original entry on oeis.org

1, -3, -3, 6, -3, 6, -3, -21, 6, 6, -3, -12, -3, 6, 6, 69, -3, -12, -3, -12, 6, 6, -3, 51, 6, 6, -21, -12, -3, -3, -3, -201, 6, 6, 6, 33, -3, 6, 6, 51, -3, -3, -3, -12, -12, 6, -3, -156, 6, -12, 6, -12, -3, 51, 6, 51, 6, 6, -3, 15, -3, 6, -12, 591, 6, -3, -3, -12, 6, -3
Offset: 1

Views

Author

Ilya Gutkovskiy, Jan 29 2022

Keywords

Crossrefs

Cf. A261582, A316441, A339718, A349922, A351023.
Showing 1-8 of 8 results.

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