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

Author

R. Muller

Keywords

• nonn

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

Crossrefs

Cf. A001751, A006882.

Programs

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 *)