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

%I A135504 #40 Jun 23 2025 14:32:38
%S A135504 1,3,6,18,108,216,1728,3456,6912,41472,497664,995328,13934592,
%T A135504 27869184,167215104,334430208,6019743744,12039487488,240789749760,
%U A135504 481579499520,963158999040,11557907988480,277389791723520,554779583447040
%N A135504 a(1)=1; for n>1, a(n) = a(n-1) + lcm(a(n-1),n).
%C A135504 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.
%C A135504 See A135506 for more comments and references.
%C A135504 Partial sums of A074179. - _David Radcliffe_, Jun 23 2025
%H A135504 T. D. Noe, <a href="/A135504/b135504.txt">Table of n, a(n) for n=1..100</a>
%t A135504 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 *)
%t A135504 RecurrenceTable[{a[1]==1,a[n]==a[n-1]+LCM[a[n-1],n]},a,{n,30}] (* _Harvey P. Dale_, Mar 03 2013 *)
%o A135504 (PARI) x1=1;for(n=2,40,x2=x1+lcm(x1,n);t=x1;x1=x2;print1(x2,","))
%o A135504 (Haskell)
%o A135504 a135504 n = a135504_list !! (n-1)
%o A135504 a135504_list = 1 : zipWith (+)
%o A135504                    a135504_list (zipWith lcm a135504_list [2..])
%o A135504 -- _Reinhard Zumkeller_, Oct 03 2012
%o A135504 (Python)
%o A135504 from sympy import lcm
%o A135504 l=[0, 1]
%o A135504 for n in range(2, 101):
%o A135504     x=l[n - 1]
%o A135504     l.append(x + lcm(x, n))
%o A135504 print(l) # _Indranil Ghosh_, Jun 27 2017
%Y A135504 Cf. A074179, A135506, A361460, A361461, A361463, A361464, A361470.
%Y A135504 Cf. also A106108.
%K A135504 nonn,nice
%O A135504 1,2
%A A135504 _Benoit Cloitre_, Feb 09 2008, Feb 10 2008