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A074179 a(1) = 1, a(n) = smallest multiple of n divisible by the sum of all previous terms.

%I A074179 #20 Jun 23 2025 17:25:59
%S A074179 1,2,3,12,90,108,1512,1728,3456,34560,456192,497664,12939264,13934592,
%T A074179 139345920,167215104,5685313536,6019743744,228750262272,240789749760,
%U A074179 481579499520,10594748989440,265831883735040,277389791723520
%N A074179 a(1) = 1, a(n) = smallest multiple of n divisible by the sum of all previous terms.
%C A074179 First differences of A135504. - _David Radcliffe_, Jun 23 2025
%H A074179 Harvey P. Dale, <a href="/A074179/b074179.txt">Table of n, a(n) for n = 1..973</a>
%F A074179 a(n) = lcm(n, Sum_{k=1..n-1} a(k)), with a(1) = 1. - _Michel Marcus_, Nov 11 2020
%p A074179 a[1] := 1:a[2] := 2:s := 3:for n from 3 to 50 do a[n] := lcm(s,n):s := s+a[n]:od:seq(a[k],k=1..50);
%t A074179 nxt[{n_,a_,t_}]:={n+1,LCM[n+1,t],t+LCM[n+1,t]}; NestList[nxt,{1,1,1},30][[All,2]] (* _Harvey P. Dale_, Dec 06 2018 *)
%o A074179 (PARI) lista(nn) = my(va=vector(nn)); va[1]=1; for (n=2, nn, va[n] = lcm(n, vecsum(va))); va; \\ _Michel Marcus_, Nov 11 2020
%Y A074179 Cf. A057827, A135504.
%K A074179 nonn
%O A074179 1,2
%A A074179 _Amarnath Murthy_, Aug 31 2002
%E A074179 Corrected and extended by _Sascha Kurz_, Feb 12 2003