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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A290983 The arithmetic function v_6(n,6).

Original entry on oeis.org

0, 0, 1, 1, 0, 1, 2, 1, 2, 2, 3, 2, 2, 3, 4, 3, 2, 3, 5, 3, 4, 4, 6, 5, 4, 4, 7, 5, 6, 5, 8, 6, 6, 7, 9, 6, 6, 6, 10, 7, 6, 7, 11, 9, 8, 8, 12, 8, 10, 9, 13, 9, 8, 11, 14, 9, 10, 10, 15, 10, 10, 10, 16, 13, 12, 11, 17, 12, 14
Offset: 2

Views

Author

Robert Price, Aug 16 2017

Keywords

References

  • J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    v[g_, n_, h_] := (d = Divisors[n]; Max[(Floor[(d - 1 - GCD[d, g])/h] + 1)*n/d]); Table[v[6, n, 6], {n, 2, 70}]
a[n_]:=n Max[Table[(Floor[(d - 1 - GCD[d, 6])/6] + 1)/d, {d, Divisors[n]}]]; Table[a[n], {n, 2, 100}] (* Vincenzo Librandi, Aug 19 2017 *)

A291040 The arithmetic function u(n,3,2).

Original entry on oeis.org

5, 5, 3, 4, 5, 3, 5, 4, 3, 5, 5, 3, 5, 5, 3, 4, 5, 3, 5, 4, 3, 5, 5, 3, 5, 5, 3, 4, 5, 3, 5, 4, 3, 5, 5, 3, 5, 5, 3, 4, 5, 3, 5, 4, 3, 5, 5, 3, 5, 5, 3, 4, 5, 3, 5, 4, 3, 5, 5, 3, 5, 5, 3, 4, 5, 3, 5, 4, 3, 5
Offset: 1

Views

Author

Robert Price, Aug 16 2017

Keywords

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    u[n_, m_, h_] := (d = Divisors[n]; Min[(h*Ceiling[m/d] - h + 1)*d]); Table[u[n, 3, 2], {n, 1, 70}]

A291267 The arithmetic function v_2(n,3).

Original entry on oeis.org

0, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 6, 5, 6, 6, 6, 8, 7, 8, 8, 8, 10, 8, 9, 9, 10, 12, 10, 10, 12, 12, 14, 12, 12, 12, 13, 16, 14, 14, 14, 16, 18, 16, 16, 16, 16, 20, 18, 17, 18, 18, 22, 18, 19, 20, 20, 24, 20, 20, 21, 21, 26, 24, 22, 24, 24, 28
Offset: 2

Views

Author

Robert Price, Aug 21 2017

Keywords

References

  • J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    v[g_, n_, h_] := (d = Divisors[n]; Max[(Floor[(d - 1 - GCD[d, g])/h] + 1)*n/d]); Table[v[2, n, 3], {n, 2, 70}]

A291268 The arithmetic function v_3(n,2).

Original entry on oeis.org

1, 0, 2, 2, 3, 3, 4, 3, 5, 5, 6, 6, 7, 6, 8, 8, 9, 9, 10, 9, 11, 11, 12, 12, 13, 12, 14, 14, 15, 15, 16, 15, 17, 17, 18, 18, 19, 18, 20, 20, 21, 21, 22, 21, 23, 23, 24, 24, 25, 24, 26, 26, 27, 27, 28, 27, 29, 29, 30, 30, 31, 30, 32, 32, 33, 33, 34, 33, 35
Offset: 2

Views

Author

Robert Price, Aug 21 2017

Keywords

References

  • J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    v[g_, n_, h_] := (d = Divisors[n]; Max[(Floor[(d - 1 - GCD[d, g])/h] + 1)*n/d]); Table[v[3, n, 2], {n, 2, 70}]

Formula

a(n) = (n + gcd(n,6) - 2*gcd(n,3))/2. - Ridouane Oudra, Feb 17 2025
Sum_{n>=4} (-1)^(n+1)/a(n) = 1 - Pi/(6*sqrt(3)) - log(3)/2. - Amiram Eldar, Feb 20 2025

A291270 The arithmetic function v_4(n,3).

Original entry on oeis.org

0, 1, 0, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 6, 4, 6, 6, 6, 8, 7, 8, 8, 8, 10, 8, 9, 8, 10, 12, 10, 10, 12, 12, 14, 12, 12, 12, 13, 16, 14, 14, 14, 16, 18, 16, 16, 16, 16, 20, 18, 16, 18, 18, 22, 18, 19, 20, 20, 24, 20, 20, 21, 20, 26, 24, 22, 24, 24, 28
Offset: 2

Views

Author

Robert Price, Aug 21 2017

Keywords

References

  • J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    v[g_, n_, h_] := (d = Divisors[n]; Max[(Floor[(d - 1 - GCD[d, g])/h] + 1)*n/d]); Table[v[4, n, 3], {n, 2, 70}]

A291271 The arithmetic function v_4(n,2).

Original entry on oeis.org

0, 1, 0, 2, 2, 3, 2, 4, 4, 5, 4, 6, 6, 7, 6, 8, 8, 9, 8, 10, 10, 11, 10, 12, 12, 13, 12, 14, 14, 15, 14, 16, 16, 17, 16, 18, 18, 19, 18, 20, 20, 21, 20, 22, 22, 23, 22, 24, 24, 25, 24, 26, 26, 27, 26, 28, 28, 29, 28, 30, 30, 31, 30, 32, 32, 33, 32, 34, 34
Offset: 2

Views

Author

Robert Price, Aug 21 2017

Keywords

Comments

For any integer n>=7, a(n) is the smallest number of diametrical slices needed to divide two pizzas equally between n-4 people. - Jamil Silva, Mar 29 2025

References

  • J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).

Links

Crossrefs

Cf. A244009, A289435, A289436, A289437, A289438, A289439, A289440, A289441.
Cf. A291330.

Programs

  • Maple
    seq((n-gcd(n,4))/2, n=2..80); # Ridouane Oudra, Dec 28 2024
  • Mathematica
    v[g_, n_, h_] := (d = Divisors[n]; Max[(Floor[(d - 1 - GCD[d, g])/h] + 1)*n/d]); Table[v[4, n, 2], {n, 2, 70}]

Formula

Conjecture: a(n) = (n-2-cos(n*Pi)-cos(n*Pi/2))/2. - Wesley Ivan Hurt, Oct 02 2017
a(n) = (n-gcd(n,4))/2 = A291330(n)/2. - Ridouane Oudra, Dec 28 2024
Sum_{n>=5} (-1)^n/a(n) = 1 - log(2) (A244009). - Amiram Eldar, Jan 15 2025
a(2)=a(4)=0, a(3)=1, a(5)=a(6)=2, a(2n+5)=n+2, a(4n+4)=2n, a(4n+6)=2n+2. - Jamil Silva, Mar 29 2025

A291272 The arithmetic function v_5(n,4).

Original entry on oeis.org

1, 1, 2, 0, 3, 2, 4, 3, 5, 3, 6, 3, 7, 5, 8, 4, 9, 5, 10, 7, 11, 6, 12, 5, 13, 9, 14, 7, 15, 8, 16, 11, 17, 10, 18, 9, 19, 13, 20, 10, 21, 11, 22, 15, 23, 12, 24, 14, 25, 17, 26, 13, 27, 15, 28, 19, 29, 15, 30, 15, 31, 21, 32, 15, 33, 17, 34, 23, 35
Offset: 2

Views

Author

Robert Price, Aug 21 2017

Keywords

References

  • J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    v[g_, n_, h_] := (d = Divisors[n]; Max[(Floor[(d - 1 - GCD[d, g])/h] + 1)*n/d]); Table[v[5, n, 4], {n, 2, 70}]

A291273 The arithmetic function v_5(n,3).

Original entry on oeis.org

1, 1, 2, 0, 3, 2, 4, 3, 5, 4, 6, 4, 7, 5, 8, 6, 9, 6, 10, 7, 11, 8, 12, 7, 13, 9, 14, 10, 15, 10, 16, 12, 17, 10, 18, 12, 19, 13, 20, 14, 21, 14, 22, 15, 23, 16, 24, 16, 25, 18, 26, 18, 27, 20, 28, 19, 29, 20, 30, 20, 31, 21, 32, 20, 33, 22, 34, 24, 35
Offset: 2

Views

Author

Robert Price, Aug 21 2017

Keywords

References

  • J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    v[g_, n_, h_] := (d = Divisors[n]; Max[(Floor[(d - 1 - GCD[d, g])/h] + 1)*n/d]); Table[v[5, n, 3], {n, 2, 70}]

A291304 The arithmetic function v_5(n,2).

Original entry on oeis.org

1, 1, 2, 0, 3, 3, 4, 4, 5, 5, 6, 6, 7, 5, 8, 8, 9, 9, 10, 10, 11, 11, 12, 10, 13, 13, 14, 14, 15, 15, 16, 16, 17, 15, 18, 18, 19, 19, 20, 20, 21, 21, 22, 20, 23, 23, 24, 24, 25, 25, 26, 26, 27, 25, 28, 28, 29, 29, 30, 30, 31, 31, 32, 30, 33, 33, 34, 34, 35
Offset: 2

Views

Author

Robert Price, Aug 21 2017

Keywords

References

  • J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441, A001622.

Programs

  • Mathematica
    v[g_, n_, h_] := (d = Divisors[n]; Max[(Floor[(d - 1 - GCD[d, g])/h] + 1)*n/d]); Table[v[5, n, 2], {n, 2, 70}]

Formula

a(n) = (n + gcd(n,10) - 2*gcd(n,5))/2. - Ridouane Oudra, Feb 17 2025
Sum_{n>=6} (-1)^(n+1)/a(n) = 1/2 - sqrt(1-2/sqrt(5))*Pi/10 + sqrt(5)*log(phi)/10 - log(5)/4, where phi is the golden ratio (A001622). - Amiram Eldar, Feb 20 2025

A291305 The arithmetic function v_5(n,1).

Original entry on oeis.org

1, 2, 3, 0, 5, 6, 7, 8, 5, 10, 11, 12, 13, 10, 15, 16, 17, 18, 15, 20, 21, 22, 23, 20, 25, 26, 27, 28, 25, 30, 31, 32, 33, 30, 35, 36, 37, 38, 35, 40, 41, 42, 43, 40, 45, 46, 47, 48, 45, 50, 51, 52, 53, 50, 55, 56, 57, 58, 55, 60, 61, 62, 63, 60, 65, 66, 67, 68, 65
Offset: 2

Views

Author

Robert Price, Aug 21 2017

Keywords

References

  • J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.
Cf. A109009.

Programs

  • Maple
    seq(n-gcd(n,5), n=2..100); # Ridouane Oudra, Dec 15 2024
  • Mathematica
    v[g_, n_, h_] := (d = Divisors[n]; Max[(Floor[(d - 1 - GCD[d, g])/h] + 1)*n/d]); Table[v[5, n, 1], {n, 2, 70}]

Formula

a(n) = n - gcd(n,5) = n - A109009(n). - Ridouane Oudra, Dec 15 2024
Previous Showing 21-30 of 113 results. Next

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