A128557 a(n) = the largest positive integer k such that (n!/k!) has at least n divisors.

1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 8, 10, 10, 11, 13, 14, 14, 15, 16, 17, 19, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 34, 35, 35, 37, 38, 39, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 49, 51, 52, 53, 54, 55, 55, 57, 57, 59, 59, 61, 62, 63, 63, 64, 65, 67, 67, 69, 69

Offset

1,4

Links

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

Example

a(11) = 8 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[nops(A)]; end: seq(a(n), n=1..90); # Emeric Deutsch, Mar 23 2007

Crossrefs

Cf. A128558, A128559.

Sequence in context: A274016 A291572 A265541 * A265542 A103303 A297232

Adjacent sequences: A128554 A128555 A128556 * A128558 A128559 A128560

Keyword

nonn

Author

Leroy Quet, Mar 10 2007

Extensions

More terms from Emeric Deutsch, Mar 23 2007

Status

approved