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 1-5 of 5 results.

A126261 a(n) is the numerator of the sum of the reciprocals of the positive integers k, k<=n, where every positive integer <= k and coprime to k is also coprime to n.

Original entry on oeis.org

1, 3, 11, 7, 137, 5, 363, 49, 19, 37, 83711, 7, 1145993, 167, 19, 1321, 42142223, 65, 275295799, 19, 43, 2887, 444316699, 133, 127, 1177, 18469, 85, 9227046511387, 23, 290774257297357, 3877999, 212, 22737, 971, 229, 2040798836801833, 233731, 1039
Offset: 1

Views

Author

Leroy Quet, Dec 22 2006

Keywords

Examples

			The positive integers k, k <= 6, where every positive integer <=k and coprime to k is also coprime to 6, are 1,2,6. So a(6) = 5 is the numerator of 1 +1/2 +1/6 = 5/3.

Crossrefs

Cf. A126260, A126262.

Programs

  • Mathematica
    f[n_] := Select[Range[n], GCD[ #, n] == 1 &];g[n_] := Plus @@ (1/# &) /@ Select[Range[n], Times @@ GCD[f[ # ], n] == 1 &];Table[Numerator[g[n]], {n, 40}] (* Ray Chandler, Dec 24 2006 *)

Extensions

Extended by Ray Chandler, Dec 24 2006

A126262 a(n) is the denominator of the sum of the reciprocals of the positive integers k, k<=n, where every positive integer <= k and coprime to k is also coprime to n.

Original entry on oeis.org

1, 2, 6, 4, 60, 3, 140, 24, 9, 20, 27720, 4, 360360, 84, 10, 560, 12252240, 36, 77597520, 10, 21, 1320, 118982864, 72, 50, 520, 7560, 42, 2329089562800, 15, 72201776446800, 1441440, 99, 9520, 420, 120, 485721041551200, 95760, 468, 24, 19914562703599200
Offset: 1

Views

Author

Leroy Quet, Dec 22 2006

Keywords

Examples

			The positive integers k, k <= 6, where every positive integer <=k and coprime to k is also coprime to 6, are 1,2,6. So a(6) = 3 is the denominator of 1 +1/2 +1/6 = 5/3.

Crossrefs

Cf. A126260, A126261.

Programs

  • Mathematica
    f[n_] := Select[Range[n], GCD[ #, n] == 1 &];g[n_] := Plus @@ (1/# &) /@ Select[Range[n], Times @@ GCD[f[ # ], n] == 1 &];Table[Denominator[g[n]], {n, 41}] (* Ray Chandler, Dec 24 2006 *)

Extensions

Extended by Ray Chandler, Dec 24 2006

A124675 a(n) = product of the positive integers k, k<= n, such that the positive integers <= k and coprime to k are also coprime to n.

Original entry on oeis.org

1, 2, 6, 8, 120, 12, 5040, 384, 324, 80, 39916800, 144, 6227020800, 672, 90, 10321920, 355687428096000, 2592, 121645100408832000, 1600, 756, 84480, 25852016738884976640000, 62208, 9000000, 1198080, 14285134080, 18816
Offset: 1

Views

Author

Leroy Quet, Dec 24 2006

Keywords

Examples

			The positive integers k, k <= 6, where the positive integers <= k and coprime to k are also coprime to 6, are 1,2,6. So a(6) = 1*2*6 = 12.

Crossrefs

Cf. A126260, A124611.

Programs

  • Mathematica
    f[n_] := Select[Range[n], GCD[ #, n] == 1 &];g[n_] := Select[Range[n], Times @@ GCD[f[ # ], n] == 1 &];Times @@@ Table[g[n], {n, 30}] (* Ray Chandler, Dec 24 2006 *)

Extensions

Extended by Ray Chandler, Dec 24 2006

A124676 a(n) = largest integer < n such that the positive integers <= a(n) and coprime to a(n) are also coprime to n.

Original entry on oeis.org

1, 2, 2, 4, 2, 6, 6, 6, 4, 10, 6, 12, 6, 3, 14, 16, 12, 18, 10, 6, 10, 22, 18, 20, 12, 24, 14, 28, 2, 30, 30, 9, 16, 5, 30, 36, 18, 12, 30, 40, 6, 42, 22, 30, 22, 46, 42, 42, 40, 15, 26, 52, 48, 10, 42, 18, 28, 58, 30, 60, 30, 42, 62, 10, 6, 66, 34, 21, 4, 70, 66, 72, 36, 60, 38, 7, 12
Offset: 2

Views

Author

Leroy Quet, Dec 24 2006

Keywords

Examples

			The positive integers k, k <= 6, where the positive integers <= k and coprime to k are also coprime to 6, are 1,2,6. So a(6) = the largest of these < 6, which is 2.

Crossrefs

Cf. A126260, A073353.

Programs

  • Mathematica
    f[n_] := Select[Range[n], GCD[ #, n] == 1 &];g[n_] := Select[Range[n - 1], Times @@ GCD[f[ # ], n] == 1 &];Max /@ Table[g[n], {n, 2, 80}] (* Ray Chandler, Dec 24 2006 *)

Extensions

Extended by Ray Chandler, Dec 24 2006

A124693 a(1)=1. a(n+1) = sum a(k), where the sum is over all positive integers k, k <= n, where each positive integer <= k and coprime to k is also coprime to n.

Original entry on oeis.org

1, 1, 2, 4, 6, 14, 16, 44, 64, 82, 88, 322, 338, 982, 1002, 1006, 2456, 6428, 6766, 19622, 19710, 19728, 19874, 98556, 105322, 126042, 126510, 252610, 253612, 1061208, 1061210, 3183626, 4770276, 4770358, 4772814, 4772828, 5939358, 31392886
Offset: 1

Views

Author

Leroy Quet, Dec 25 2006

Keywords

Examples

			The positive integers k, where k <= 6 and where each positive integer <= k and coprime to k is also coprime to 6, are 1,2,6. So a(7) = a(1)+a(2)+a(6) = 1+1+14 = 16.

Crossrefs

Cf. A126260.

Programs

  • Mathematica
    f[n_] := Select[ Range[n], GCD[ #, n] == 1 &]; g[n_] := Select[ Range[n], Times @@ GCD[f[ # ], n] == 1 &]; h[l_List] := Append[l, Plus @@ l[[g[Length[l]]]]]; Nest[h, {1}, 38] (* Ray Chandler, Dec 26 2006 *)

Extensions

Extended by Ray Chandler, Dec 26 2006
Showing 1-5 of 5 results.

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