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.

A082452 a(n)=2n+1 where n is such that A083344(n) is not zero.

Original entry on oeis.org

45, 75, 117, 147, 189, 195, 225, 231, 245, 315, 325, 345, 363, 385, 405, 441, 483, 495, 507, 525, 561, 567, 585, 595, 645, 663, 675, 693, 715, 735, 765, 775, 777, 795, 819, 845, 847, 867, 875, 891, 931, 945, 957, 975, 1001, 1035, 1071, 1083, 1089, 1095, 1125
Offset: 1

Views

Author

Labos Elemer, Apr 25 2003

Keywords

Examples

			n=22: 2n+1=45, A057643(45)=5520, a(22)=GCD[45,5520]=15 while A066715[45]=3; a(22)=15-3=12.

Crossrefs

Cf. A057643, A066715, A000203, A082457, A083344.

Programs

  • Mathematica
    di[x_] := Apply[LCM, Divisors[x]+1] (*A066715=*)t1=Table[GCD[2*n+1, DivisorSigma[1, 2*n+1]], {n, 1, 2048}]; (*A082457=*)t2=Table[GCD[2*w+1, di[1+2*w]], {w, 1, 2048}]; (*A083344=*)t3=t2-t1; (*A082452=*)1+2*Flatten[Position[Abs[Sign[t3]], 1]];

A082453 a(n)=2n+1 where n is such that A083344(n) is zero.

Original entry on oeis.org

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137
Offset: 1

Views

Author

Labos Elemer, Apr 25 2003

Keywords

Examples

			First two missing odd numbers are 45 and 75; missing terms are in A082452.

Crossrefs

Cf. A057643, A066715, A000203, A082457, A083344.

Programs

  • Mathematica
    di[x_] := Apply[LCM, Divisors[x]+1] (*A066715=*)t1=Table[GCD[2*n+1, DivisorSigma[1, 2*n+1]], {n, 1, 2048}]; (*A082457=*)t2=Table[GCD[2*w+1, di[1+2*w]], {w, 1, 2048}]; (*A083344=*)t3=t2-t1; (*A082453=*)1+2*Flatten[Position[Abs[Sign[t3]], 0]];

A082457 a(n) = gcd(1+2n, A057643(1+2n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 15, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 7, 1, 5, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 15, 1, 1, 3, 1, 5, 1, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 7, 1, 1, 15, 1, 1, 1, 1, 1, 3, 1, 1
Offset: 1

Views

Author

Labos Elemer, Apr 25 2003

Keywords

Comments

This and A066715 are mostly equal; for differences see A083344.

Examples

			n=22: 2n+1=45, A057643(45)=5520, a(22)=gcd(45,5520)=15 while A066715(45)=3.

Crossrefs

Cf. A057643, A066715, A000203, A083344.

Programs

  • Mathematica
    di[x_] := Apply[LCM, Divisors[x]+1] Table[GCD[2*w+1, di[1+2*w]], {w, 1, 2048}];
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.