A135504 a(1)=1; for n>1, a(n) = a(n-1) + lcm(a(n-1),n).

1, 3, 6, 18, 108, 216, 1728, 3456, 6912, 41472, 497664, 995328, 13934592, 27869184, 167215104, 334430208, 6019743744, 12039487488, 240789749760, 481579499520, 963158999040, 11557907988480, 277389791723520, 554779583447040

Offset

1,2

Comments

This sequence has properties related to primes. For instance: a(n+1)/a(n)-1 consists of 1's or primes only. Any prime p>=3 divides a(n) for the first time when n=p*w(p)-1 where w(p) is the least positive integer such that p*w(p)-1 is prime.

See A135506 for more comments and references.

Links

T. D. Noe, Table of n, a(n) for n=1..100

Mathematica

a[1] = 1; a[n_] := a[n] = a[n-1] + LCM[a[n-1], n]; Table[a[n], {n, 1, 24}] (* Jean-François Alcover, Dec 16 2011 *)
RecurrenceTable[{a[1]==1, a[n]==a[n-1]+LCM[a[n-1], n]}, a, {n, 30}] (* Harvey P. Dale, Mar 03 2013 *)

Prog

(PARI) x1=1; for(n=2, 40, x2=x1+lcm(x1, n); t=x1; x1=x2; print1(x2, ", "))
(Haskell)
a135504 n = a135504_list !! (n-1)
a135504_list = 1 : zipWith (+)
                   a135504_list (zipWith lcm a135504_list [2..])
-- Reinhard Zumkeller, Oct 03 2012
(Python)
from sympy import lcm
l=[0, 1]
for n in range(2, 101):
    x=l[n - 1]
    l.append(x + lcm(x, n))
print(l) # Indranil Ghosh, Jun 27 2017

Crossrefs

Cf. A135506, A361460, A361461, A361463, A361464, A361470.

Cf. also A106108.

Sequence in context: A038060 A366607 A345134 * A307334 A057268 A085401

Adjacent sequences: A135501 A135502 A135503 * A135505 A135506 A135507

Keyword

nonn,nice

Author

Benoit Cloitre, Feb 09 2008, Feb 10 2008

Status

approved