A217662 For n > 2 , a(n) = a(n-2) + lcm(a(n-2), n-1) with a(1)=2, a(2)=2.

2, 2, 4, 8, 8, 48, 32, 384, 64, 1536, 384, 18432, 768, 258048, 6144, 1548288, 12288, 27869184, 49152, 557383680, 294912, 1114767360, 3538944, 26754416640, 7077888, 160526499840, 99090432, 321052999680, 198180864, 9631589990400, 1189085184, 308210879692800

Offset: 1

Author

Pedja Terzic, Oct 10 2012

Keywords

• nonn

Comments

A217663(n) = a(n+2)/a(n)-1 consists of 1's and primes only.

Crossrefs

Cf. A135504.

Programs

Mathematica

RecurrenceTable[{a[n]==a[n-2]+LCM[n-1,a[n-2]],a[1] == 2,a[2]==2},a,{n,1, 24}]
t = {2, 2}; Do[AppendTo[t, t[[-2]] + LCM[n-1, t[[-2]]]], {n, 3, 40}]; t (* T. D. Noe, Oct 10 2012 *)
nxt[{n_,a_,b_}]:={n+1,b,a+LCM[a,n]}; NestList[nxt,{2,2,2},40][[All,2]] (* Harvey P. Dale, Aug 20 2020 *)

Formula

For prime p > 2, a(p+1) = (p+1)*a(p-1), which proves the statement in A217663. - M. F. Hasler, Oct 11 2012