A007922 Smallest k such that k!! is a multiple of n.

1, 2, 3, 4, 5, 6, 7, 4, 9, 10, 11, 6, 13, 14, 5, 6, 17, 12, 19, 10, 7, 22, 23, 6, 15, 26, 9, 14, 29, 10, 31, 8, 11, 34, 7, 12, 37, 38, 13, 10, 41, 14, 43, 22, 9, 46, 47, 6, 21, 20, 17, 26, 53, 18, 11, 14, 19, 58, 59, 10, 61, 62, 9, 8, 13, 22, 67, 34, 23, 14, 71, 12, 73, 74, 15, 38, 11, 26

Offset

1,2

Comments

a(n) <= n, with equality if n is 1, 9, a prime or twice a prime. Are those the only cases of equality? - Robert Israel, Apr 22 2024

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

F. Smarandache, Only Problems, Not Solutions!.

Index entries for sequences related to factorial numbers

Maple

V:= Vector(100): count:= 0:
S:= {$1..100}:
for k from 1 while count < 100 do
  v:= doublefactorial(k);
  SP:= select(t -> v mod t = 0, S);
  count:= count + nops(SP);
  V[convert(SP, list)]:= k;
  S:= S minus SP;
od:
convert(V, list); # Robert Israel, Apr 21 2024

Mathematica

df[n_]:=Module[{k=1}, While[!Divisible[k!!, n], k++]; k]; Array[df, 80] (* Harvey P. Dale, Jun 04 2013 *)

Crossrefs

Cf. A001751, A006882.

Sequence in context: A332230 A319999 A083501 * A007948 A355261 A353897

Adjacent sequences: A007919 A007920 A007921 * A007923 A007924 A007925

Keyword

nonn

Author

R. Muller

Status

approved