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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

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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.

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

LINKS

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

Benoit Cloitre, Primes in LCM recurrences: a density theorem via companion sieves, arXiv:2510.18891 [math.NT], 2025. See p. 2.

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)