OFFSET
1,2
COMMENTS
Group the natural numbers so that every 2n-th group product is divisible by the single number in the next group. (1), (2,3,4,5), (6), (7,8,9,10,11), (12), (13,14,15,16,17,18,19),(20), (21,22,23,24,25,26,27),(28),...Sequence contains the ratio of the product of terms in 2n-th group and the (2n+1)-th group.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10001 (corrected by Robert Israel, Jan 20 2019)
EXAMPLE
a(1) = 1*2*3*4*5/6 = 20, a(2) = 7*8*9*10*11/12 = 4620, a(3) = 13*14*15*16*17*18*19/20 = 12697776, a(4) = 159845400 = 21*22*...*27/28.
MAPLE
t:= 0:
for n from 1 to 30 do
p:= t+1;
for j from t+2 while not (p/j)::integer do p:= p*j od;
A[n]:= p/j;
t:= j;
od:
seq(A[i], i=1..30); # Robert Israel, Jul 16 2018
MATHEMATICA
a[1] = 1; t = 0; nmax = 16; For[n = 1, n <= nmax, n++, p = t+1; For[j = t+2, Not[IntegerQ[p/j]], j++, p = p*j]; a[n+1] = p/j; t = j];
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Mar 25 2019, after Robert Israel *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jan 10 2003
EXTENSIONS
More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com) and Sascha Kurz, Jan 12 2003
Edited by N. J. A. Sloane, Nov 04 2018 at the suggestion of Georg Fischer. This entry now contains the merger of two identical sequences submitted by the same author.
STATUS
approved