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 1-2 of 2 results.

A322445 Smallest positive integer m such that n divides A297707(m).

Original entry on oeis.org

1, 2, 3, 4, 5, 3, 7, 4, 3, 5, 11, 4, 13, 7, 5, 4, 17, 3, 19, 5, 7, 11, 23, 4, 5, 13, 6, 7, 29, 5, 31, 4, 11, 17, 7, 5, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 4, 7, 5, 17, 13, 53, 6, 11, 7, 19, 29, 59, 5, 61, 31, 7, 4, 13
Offset: 1

Views

Author

Lechoslaw Ratajczak, Dec 08 2018

Keywords

Comments

If p is prime, a(p) = p.
The first three integers n for which a(n!) is not a prime number are: 1 (a(1!) = 1), 4 (a(4!) = 4), 10 (a(10!) = 8). Is there a larger n? If such a number n exists, it is greater than 2000.
The smallest integer n satisfying the equation a(n) = a(n+1) is 2400 (a(2400) = a(2401) = 7). Is there a larger n? If such a number n exists, it is greater than 3000.

Examples

			a(12) = 4 because 12 is not divisible by A297707(1) = 1, A297707(2) = 2*1, A297707(3) = 3*2*1*3*1, and is divisible by A297707(4) = 4*3*2*1*4*2*4*1.
		

Crossrefs

Programs

  • Mathematica
    f[n_] := n^(n - 1) *  Product[k^DivisorSigma[0, n - k], {k, n - 1}]; a[n_] := Module[{k = 1}, While[! Divisible[f[k], n], k++]; k]; Array[a, 60] (* Amiram Eldar, Dec 08 2018 *)
  • PARI
    f(n) = (n^(n-1))*prod(k=1, n-1, k^numdiv(n-k)); \\ A297707
    a(n) = {my(k=1); while (f(k) % n, k++); k;} \\ Michel Marcus, Dec 09 2018

A064778 Largest m such that 1..m all divide n!.

Original entry on oeis.org

1, 2, 3, 4, 6, 6, 10, 10, 10, 10, 12, 12, 16, 16, 16, 16, 18, 18, 22, 22, 22, 22, 28, 28, 28, 28, 28, 28, 30, 30, 36, 36, 36, 36, 36, 36, 40, 40, 40, 40, 42, 42, 46, 46, 46, 46, 52, 52, 52, 52, 52, 52, 58, 58, 58, 58, 58, 58, 60, 60, 66, 66, 66, 66, 66, 66, 70, 70, 70, 70, 72
Offset: 1

Views

Author

Robert G. Wilson v, Oct 18 2001

Keywords

Comments

Also the largest m such that 1!..m! all divide 2*A297707(n). - Lechoslaw Ratajczak, Apr 23 2019

Crossrefs

Programs

  • Mathematica
    Do[ m = 1; While[ IntegerQ[n!/m], m++ ]; Print[m - 1], {n, 1, 100} ]
    Table[Position[Divisible[n!,Range[100]],False,1,1][[1]]-1,{n,80}]//Flatten (* Harvey P. Dale, Aug 02 2024 *)
  • PARI
    { m=2; for (n=1, 1000, while (n!%m == 0, m++); write("b064778.txt", n, " ", m - 1) ) } \\ Harry J. Smith, Sep 24 2009

Formula

a(n) = A151800(n) - 1 for n != 3. - David A. Corneth, Apr 23 2019
Showing 1-2 of 2 results.