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 1-4 of 4 results.

A337609 Positive integers m such that A126286^k(m) = m for some positive integer k.

Original entry on oeis.org

2, 3, 14, 21, 26, 34, 38, 39, 50, 57, 62, 74, 75, 85, 86, 93, 94, 98, 110, 111, 118, 122, 129, 134, 142, 146, 147, 154, 158, 165, 170, 182, 183, 194, 201, 202, 206, 214, 218, 219, 230, 235, 237, 242, 254, 255, 266, 273, 274, 278, 286, 290, 291, 298, 302, 309
Offset: 1

Views

Author

Ely Golden, Oct 07 2020

Keywords

Comments

A126286^k(m) means apply A126286 to m k times.
Equivalently, the numbers that belong to a cycle under the map x -> A126286(x).
For any term m in this sequence, A126286(A126286(m)) = m.
Supersequence of A017545. Moreover, this sequence can be represented as an infinite union of arithmetic progressions.
2 and 3 are the only primes in this sequence.

Examples

			3 is a term since A126286(A126286(3)) = A126286(2) = 3.

Links

Crossrefs

Cf. A017545, A126286, A337610, A337611, A337612.

A126287 a(1) = 1, a(2) = 1, a(n) = n * LeastPrimeFactor(n-1) / LeastPrimeFactor(n).

Original entry on oeis.org

1, 1, 2, 6, 2, 15, 2, 28, 6, 15, 2, 66, 2, 91, 10, 24, 2, 153, 2, 190, 14, 33, 2, 276, 10, 65, 18, 42, 2, 435, 2, 496, 22, 51, 14, 90, 2, 703, 26, 60, 2, 861, 2, 946, 30, 69, 2, 1128, 14, 175, 34, 78, 2, 1431, 22, 140, 38, 87, 2, 1770, 2, 1891, 42, 96, 26, 165, 2, 2278, 46, 105
Offset: 1

Views

Author

Lior Manor, Dec 25 2006

Keywords

Examples

			a(6) = 6 * LeastPrimeFactor(5) / LeastPrimeFactor(6) = 6 * 5 / 2 = 15

Links

Crossrefs

Cf. A126286, A126288, A126289, A020639.

Programs

  • Maple
    N:= 1000: # to get a(1) to a(n)
a[1]:= 1: a[2]:= 1:
b:= 2:
for n from 3 to N do
c:= min(numtheory:-factorset(n));
a[n]:= n*b/c;
b:= c;
od:
seq(a[n],n=1..N); # Robert Israel, May 20 2015
  • Mathematica
    a[1] := 1; a[2] := 1; a[n_] := n*FactorInteger[n - 1][[1, 1]]/FactorInteger[n][[1, 1]]; Table[a[n], {n, 70}] (* Ivan Neretin, May 20 2015 *)

Formula

a(n) = A032742(n)*A020639(n-1), for n>2. - Michel Marcus, May 20 2015

A126288 a(1) = 2, a(n) = n * LargestPrimeFactor(n+1) / LargestPrimeFactor(n).

Original entry on oeis.org

2, 3, 2, 10, 3, 14, 2, 12, 15, 22, 3, 52, 7, 10, 6, 136, 3, 114, 5, 28, 33, 46, 3, 40, 65, 6, 63, 116, 5, 186, 2, 176, 51, 14, 15, 444, 19, 26, 15, 328, 7, 258, 11, 20, 207, 94, 3, 112, 35, 170, 39, 212, 3, 198, 35, 152, 87, 118, 5, 732, 31, 14, 18, 416, 55, 402, 17, 92, 21, 710
Offset: 1

Views

Author

Lior Manor, Dec 25 2006

Keywords

Examples

			a(6) = 6 * LargestPrimeFactor(7) / LargestPrimeFactor(6) = 6 * 7 / 3 = 14

Links

Crossrefs

Cf. A126286, A126287, A126289, A006530.

Programs

  • Mathematica
    a[1] := 2; a[n_] := n*FactorInteger[n + 1][[-1, 1]]/FactorInteger[n][[-1, 1]]; Table[a[n], {n, 70}] (* Ivan Neretin, May 20 2015 *)
  • PARI
    gpf(n) = vecmax(factor(n)[,1]);
a(n) = if (n==1, 2, n*gpf(n+1)/gpf(n)); \\ Michel Marcus, Sep 08 2020

Formula

a(n) = A006530(n+1)*A052126(n) for n>1. - Michel Marcus, May 20 2015

A126289 a(1) = 1, a(2) = 1, a(n) = n * LargestPrimeFactor(n-1) / LargestPrimeFactor(n).

Original entry on oeis.org

1, 1, 2, 6, 2, 10, 3, 28, 6, 6, 5, 44, 3, 26, 21, 40, 2, 102, 3, 76, 15, 14, 11, 184, 15, 10, 117, 12, 7, 174, 5, 496, 6, 22, 85, 84, 3, 74, 57, 104, 5, 246, 7, 172, 99, 10, 23, 752, 21, 70, 15, 68, 13, 954, 15, 88, 21, 38, 29, 708, 5, 122, 279, 224, 10, 78, 11, 268, 51, 230, 7
Offset: 1

Views

Author

Lior Manor, Dec 25 2006

Keywords

Examples

			a(6) = 6 * LargestPrimeFactor(5) / LargestPrimeFactor(6) = 6 * 5 / 3 = 10

Links

Crossrefs

Cf. A126286, A126287, A126288, A006530.

Programs

  • Mathematica
    a[1] := 1; a[2] := 1; a[n_] := n*FactorInteger[n - 1][[-1, 1]]/FactorInteger[n][[-1, 1]]; Table[a[n], {n, 71}] (* Ivan Neretin, May 20 2015 *)
  • PARI
    gpf(n) = vecmax(factor(n)[,1]); \\ A006530
a(n) = if (n<=2, 1, n*gpf(n-1)/gpf(n)); \\ Michel Marcus, Oct 07 2020

Formula

a(n) = A006530(n-1)*A052126(n) for n>2. - Michel Marcus, May 20 2015
Showing 1-4 of 4 results.

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