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

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

Author

Robert G. Wilson v, Oct 18 2001

Keywords

• easy
• nonn

Comments

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

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002034, A151800, A297707.

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