A092914 a(n) = (n-1)*(n-2)*...*(n-r) with the least value of r so that n divides a(n).

60, 0, 840, 20160, 15120, 0, 7920, 0, 8648640, 240240, 3603600, 0, 8910720, 0, 1395360, 390700800, 14079294028800, 0, 212520, 7117005772800, 32382376266240000, 1133836704000, 4475671200, 0, 14250600, 0, 318073392000

Offset

6,1

Comments

Analogous to the Kempner sequence A002034 where one goes forwards instead of backwards.

Least multiple of n of the form (n-1)!/k! if n is composite, 0 if n is prime.

a(1) = ... = a(5) = 0, so offset is set to 6. In fact 4 is the only composite n such that a(n) = 0. a(2p) = (2p-1)!/(p-1)! if p is a prime.

Links

Harvey P. Dale, Table of n, a(n) for n = 6..733

Example

9 divides 8*7*6*5*4*3 = 20160 but 9 does not divide 8*7*6*5*4, so a(9) = 20160.

Mathematica

Table[SelectFirst[FoldList[Times, Range[n-1, 0, -1]], Divisible[#, n]&], {n, 6, 40}] (* Harvey P. Dale, Jul 29 2015 *)

Prog

(PARI) m=32; for(n=6, m, r=1; p=n-r; while(r<=n&&p%n>0, r++; p=p*(n-r)); print1(p, ", "))

Crossrefs

Cf. A092915, A092916.

Sequence in context: A093403 A087535 A058931 * A022083 A174675 A016532

Adjacent sequences: A092911 A092912 A092913 * A092915 A092916 A092917

Keyword

nonn

Author

Amarnath Murthy, Mar 16 2004

Extensions

Edited and extended by Klaus Brockhaus, Mar 17 2004

Status

approved