A128559 a(n) is the smallest positive integer k such that n!/k! has at most n divisors.

1, 1, 2, 3, 4, 5, 6, 6, 8, 9, 9, 10, 11, 12, 14, 15, 15, 16, 17, 18, 20, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 36, 38, 39, 40, 40, 42, 43, 44, 45, 45, 47, 48, 49, 50, 50, 52, 53, 54, 55, 56, 56, 58, 58, 60, 60, 62, 63, 64, 64, 65, 66, 68, 68, 70, 70

Offset

1,3

Links

Table of n, a(n) for n=1..73.

Example

a(11) = 9 because 11!/8! = 9*10*11 = 990 has 24 divisors (and 24 is > 11), but 11!/9! = 10*11 = 110 has 8 divisors (and 8 is <= 11).

Maple

with(numtheory): a:=proc(n) local A, k: A:={}: for k from 1 to n do if tau(n!/k!)<=n then A:=A union {k} else A:=A fi od: A[1]: end: seq(a(n), n=1..90); # Emeric Deutsch, Mar 25 2007

Crossrefs

Cf. A128557.

Sequence in context: A061468 A343779 A084766 * A122168 A017856 A087412

Adjacent sequences: A128556 A128557 A128558 * A128560 A128561 A128562

Keyword

nonn

Author

Leroy Quet, Mar 10 2007

Extensions

More terms from Emeric Deutsch, Mar 25 2007

Status

approved