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 1-3 of 3 results.

A070298 Let Unrel(m) = number of unrelated numbers less than m; then a(n) = number of values of m for which Unrel(m) = n.

Original entry on oeis.org

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

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Author

Amarnath Murthy, May 10 2002

Keywords

Comments

a(0), not included in the sequence, is infinite, as no prime has any unrelated number.
Apparently this gives the indices k such that A045763(k)=n. - R. J. Mathar, Jun 27 2007

Examples

			a(1) = 3, the three numbers m being 6,8 and 9. The corresponding single unrelated numbers are 4, 6 and 6 respectively.

Links

Crossrefs

Cf. A045763, A070297.

Extensions

Corrected and extended by R. J. Mathar, Jun 27 2007
More terms from Jinyuan Wang, May 25 2020

A073764 a(n) = least number x such that A045763(x)=n or 0 if no such number exists.

Original entry on oeis.org

6, 0, 10, 15, 14, 21, 18, 35, 22, 33, 26, 39, 0, 65, 30, 36, 38, 57, 44, 95, 46, 63, 42, 115, 50, 64, 58, 87, 54, 75, 68, 155, 60, 99, 74, 111, 72, 185, 66, 117, 86, 129, 92, 215, 94, 141, 78, 235, 84, 105, 98, 100, 96, 265, 90, 135, 118, 147, 122, 183, 108, 305, 102
Offset: 1

Views

Author

Labos Elemer, Aug 08 2002

Keywords

Comments

A070297 without its term a(0). [From R. J. Mathar, Sep 23 2008]

Examples

			A045763(x)=5 first holds if x=14 because unrelated set of 14={4,6,8,10,12} has 5 entries. No solutions were found for n=2,13,67,93 when tested at <100000.

Crossrefs

Cf. A045763, A073757-A073766.

Programs

  • Mathematica
    t=Table[0, {100}]; Do[s=n+1-DivisorSigma[0, n]-EulerPhi[n]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 100000}]; t

A118657 a(n) = Sum_[k unrelated to n and k

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 0, 1, 1, 3, 0, 5, 0, 11, 10, 20, 0, 51, 0, 99, 79, 192, 0, 466, 112, 850, 612, 1767, 0, 4267, 0, 7712, 5684, 15446, 6348, 37219, 0, 68111, 49245, 142588, 0, 340698, 0, 624999, 587477, 1244507, 0, 3131628, 348903, 6214474, 4172889, 11883510, 0, 28533958, 7586253, 52606134, 36932401, 104858718, 0, 259054161
Offset: 1

Views

Author

Jonathan Vos Post, May 18 2006

Keywords

Comments

Primes include a(10) = 3, a(12) = 5, a(16) = 19, a(24) = 397. a(n) is unrelated to n for a(14) = 10, a(15) = 10, a(18) = 39, a(20) = 85, a(21) = 66, a(22) = 164.

Examples

			a(6) = 1 because 4 is the only number less than 6 which is unrelated to 6, so a(6) = a(4) = 1.
a(10) = a(4) + a(6) + a(8) = 1 + 1 + 1 = 3.
a(12) = a(8) + a(9) + a(10) = 1 + 1 + 3 = 5.

Crossrefs

See also A045763 = number of numbers "unrelated to n": mA002033; A045545; A111356 = numbers n such that the number of numbers "unrelated to n" is itself unrelated to n.
Cf. A070297.

Programs

  • Mathematica
    unr[n_, k_] := GCD[n, k] > 1 && Mod[n, k] > 0; a[1] = a[2] = a[3] = a[4] = 1;
a[n_] := a[n] = Sum[a[k] Boole[unr[n, k]], {k, n - 1}]; Array[a, 60]

Formula

For primes p>3, a(p) = 0.

Extensions

Edited by N. J. A. Sloane, Dec 03 2006
Edited and many terms corrected by Giovanni Resta, Jun 16 2016
Showing 1-3 of 3 results.

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

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