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

Author

Benoit Cloitre, Feb 09 2008, Feb 10 2008

Keywords

• nonn
• nice

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.

Partial sums of A074179. - David Radcliffe, Jun 23 2025

Links

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

Crossrefs

Cf. A074179, A135506, A361460, A361461, A361463, A361464, A361470.

Cf. also A106108.

Programs

Haskell

a135504 n = a135504_list !! (n-1)
a135504_list = 1 : zipWith (+)
                   a135504_list (zipWith lcm a135504_list [2..])
-- Reinhard Zumkeller, Oct 03 2012

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 *)

PARI

x1=1;for(n=2,40,x2=x1+lcm(x1,n);t=x1;x1=x2;print1(x2,","))

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