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A334942 a(1) = 1, a(n) = a(n-1) / gcd(a(n-1),n) if this gcd is > 1, else a(n) = 2*a(n-1) + 4.

%I A334942 #15 Aug 09 2025 01:24:20
%S A334942 1,6,2,1,6,1,6,3,1,6,16,4,12,6,2,1,6,1,6,3,1,6,16,2,8,4,12,3,10,1,6,3,
%T A334942 1,6,16,4,12,6,2,1,6,1,6,3,1,6,16,1,6,3,1,6,16,8,20,5,14,7,18,3,10,5,
%U A334942 14,7,18,3,10,5,14,1,6,1,6,3,1,6,16,8,20,1,6
%N A334942 a(1) = 1, a(n) = a(n-1) / gcd(a(n-1),n) if this gcd is > 1, else a(n) = 2*a(n-1) + 4.
%C A334942 A variant of A133058.
%e A334942 a(2) = 2*a(1) + 4 = 6, a(3) = a(2)/3 = 2, a(4) = a(3)/2 = 1, a(5) = 2*a(4) + 4 = 6, ...
%t A334942 a[1] = 1; a[n_] := a[n] = If[(g = GCD[a[n-1], n]) > 1, a[n-1]/g, 2*a[n-1] + 4]; Array[a, 100]
%o A334942 (PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, my(g = gcd(va[n-1], n)); if (g > 1, va[n] = va[n-1]/g, va[n] = 2*va[n-1] + 4);); va;} \\ _Michel Marcus_, May 17 2020
%Y A334942 Cf. A133058.
%K A334942 nonn
%O A334942 1,2
%A A334942 _Ctibor O. Zizka_, May 17 2020