A109896 -id:A109896 - cp's OEIS frontend

A079759 Let b(0)=0. For n >= 1, b(n) is the least k > b(n-1)+1 such that k divides (k-1)!/b(n-1)!, and a(n) = (b(n)-1)!/(b(n-1)!*b(n)).

1, 20, 4620, 12697776, 159845400, 941432800, 158800433792, 1895312483064000, 3438271897004237230080, 933561026438040, 2562849175892544, 640904462719404383808000, 1528364130975, 2352733350786, 959393282698730880000, 6142080926952

Offset: 1

Amarnath Murthy, Jan 10 2003

nonn

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.

			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.

Robert Israel, Table of n, a(n) for n = 1..10001 (corrected by Robert Israel, Jan 20 2019)

Cf. A079759, A079760, A109895, A109896, A109897.

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

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 *)

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.

A109895 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 single members of the odd numbered groups.

Original entry on oeis.org

1, 6, 12, 20, 28, 36, 45, 56, 70, 80, 90, 104, 112, 120, 132, 140, 154, 168, 180, 192, 208, 220, 234, 250, 264, 280, 297, 312, 324, 336, 350, 360, 378, 396, 416, 432, 448, 462, 480, 495, 504, 520, 539, 560, 576, 594, 612, 630, 640, 660, 672, 693, 714, 728, 748

Offset: 1

Amarnath Murthy, Jul 13 2005

nonn

a(n) divides (a(n)-1)! / (a(n-1)!) and is the smallest integer with this property. - Simon Nickerson (simonn(AT)maths.bham.ac.uk), Jul 15 2005

Essentially a duplicate of A079760. - R. J. Mathar, Aug 18 2008

Cf. A079759, A109896, A109897.

A := [ 1 ]; n := 1; repeat p := 1; k := n + 1; repeat p := p * k; k := k+1; until p mod k = 0; n := k; Add(A, n); until n > 10000; # Simon Nickerson

More terms from Simon Nickerson (simonn(AT)maths.bham.ac.uk), Jul 15 2005

A109897 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 product of terms in the 2n-th group.

Original entry on oeis.org

120, 55440, 253955520, 4475671200, 33891580800, 7146019520640, 106137499051584000, 240679032790296606105600, 74684882115043200, 230656425830328960, 66654064122818055916032000, 171176782669200, 282328002094320, 126639913316232476160000, 859891329773280

Offset: 1

Amarnath Murthy, Jul 13 2005

nonn

			a(2) = 7*8*9*10*11 = 55440.

Cf. A079759, A109895, A109896.

m=1;for(k=2,150,if(m%k==0,print1(m", ");m=1,m*=k))

Terms from a(5) from Franklin T. Adams-Watters, Jun 26 2011

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A079759 Let b(0)=0. For n >= 1, b(n) is the least k > b(n-1)+1 such that k divides (k-1)!/b(n-1)!, and a(n) = (b(n)-1)!/(b(n-1)!*b(n)).

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A109895 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 single members of the odd numbered groups.

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A109897 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 product of terms in the 2n-th group.

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