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.

A337611 Positive integers m such that A126288^k(m) = m for some positive integer k.

Original entry on oeis.org

2, 3, 6, 10, 14, 20, 22, 26, 28, 38, 44, 46, 52, 76, 78, 88, 94, 102, 105, 114, 116, 117, 136, 138, 152, 171, 186, 187, 195, 207, 212, 247, 248, 266, 282, 284, 285, 296, 304, 322, 333, 354, 366, 369, 387, 402, 403, 407, 414, 423, 425, 426, 430, 437, 442, 468
Offset: 1

Views

Author

Ely Golden, Sep 05 2020

Keywords

Comments

A126288^k(m) means apply A126288 to m k times.
Equivalently, the numbers that belong to a cycle under the map x -> A126288(x).
2 and 3 are the only primes in this sequence.

Examples

			3 is a term since A126288(A126288(3)) = A126288(2) = 3.

Links

Crossrefs

Cf. A337609, A337610, A337612, A126288, A052126.

Programs

  • PARI
    gpf(n) = vecmax(factor(n)[,1]);
f(n) = if (n==1, 2, n*gpf(n+1)/gpf(n)); \\ A126288
incycle(n, list) = {my(v=Vec(list)); #select(x->(x==n), v);}
cycle(n) = {my(list = List(), repeat=1); while(repeat, n = f(n); if (incycle(n, list), repeat=0); listput(list, n);); list;}
isok(n) = {my(list = cycle(n)); incycle(n, list);} \\ Michel Marcus, Sep 08 2020

Formula

For any term m, gcd {m, A126288(m), A126288(A126288(m)), ...} = A052126(m).

A126286 a(1) = 2, a(n) = n * LeastPrimeFactor(n+1) / LeastPrimeFactor(n).

Original entry on oeis.org

2, 3, 2, 10, 2, 21, 2, 12, 6, 55, 2, 78, 2, 21, 10, 136, 2, 171, 2, 30, 14, 253, 2, 60, 10, 39, 18, 406, 2, 465, 2, 48, 22, 85, 14, 666, 2, 57, 26, 820, 2, 903, 2, 66, 30, 1081, 2, 168, 14, 75, 34, 1378, 2, 135, 22, 84, 38, 1711, 2, 1830, 2, 93, 42, 160, 26, 2211, 2, 102, 46
Offset: 1

Views

Author

Lior Manor, Dec 25 2006

Keywords

Examples

			a(6) = (6 / LeastPrimeFactor(6)) * LeastPrimeFactor(7) = 21.

Links

Crossrefs

Cf. A126287, A126288, A126289, A020639.

Programs

  • Mathematica
    a[1] := 2; a[n_] := n*FactorInteger[n + 1][[1, 1]]/FactorInteger[n][[1, 1]]; Table[a[n], {n, 69}] (* Ivan Neretin, May 20 2015 *)
  • PARI
    a(n) = if (n==1, 2, n*factor(n+1)[1, 1]/factor(n)[1, 1]); \\ Michel Marcus, Aug 14 2013

Formula

a(n) = A032742(n)*A020639(n+1), for n>1. - Ivan Neretin, May 20 2015

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

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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