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.

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, 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, 14, 7, 18, 3, 10, 5, 14, 1, 6, 1, 6, 3, 1, 6, 16, 8, 20, 1, 6

Offset: 1

Author

Ctibor O. Zizka, May 17 2020

Keywords

• nonn

Comments

A variant of A133058.

Examples

			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, ...
		

Crossrefs

Cf. A133058.

Programs

Mathematica

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]

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