A334840 a(1) = 1, a(n) = a(n-1)/gcd(a(n-1),n) if this gcd is > 1, else a(n) = 4*a(n-1).
1, 4, 16, 4, 16, 8, 32, 4, 16, 8, 32, 8, 32, 16, 64, 4, 16, 8, 32, 8, 32, 16, 64, 8, 32, 16, 64, 16, 64, 32, 128, 4, 16, 8, 32, 8, 32, 16, 64, 8, 32, 16, 64, 16, 64, 32, 128, 8, 32, 16, 64, 16, 64, 32, 128, 16, 64, 32, 128, 32, 128, 64, 256, 4, 16
Offset: 1
Keywords
Examples
a(2) = 4*a(1) = 4, a(3) = 4*a(2) = 16, a(4) = a(3)/4 = 4, a(5) = 4*a(4) = 16, ...
Programs
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Magma
a:=[1]; for n in [2..70] do if Gcd(a[n-1], n) eq 1 then Append(~a,4* a[n-1]); else Append(~a, a[n-1] div Gcd(a[n-1], n)); end if; end for; a; // Marius A. Burtea, May 13 2020
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Mathematica
a[1] = 1; a[n_] := a[n] = If[(g = GCD[a[n-1], n]) > 1, a[n-1]/g, 4*a[n-1]]; Array[a, 100] (* Amiram Eldar, May 13 2020 *)
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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] = 4*va[n-1]);); va;} \\ Michel Marcus, May 17 2020 -
Python
from itertools import count, islice from math import gcd def A334840_gen(): # generator of terms yield (a:=1) for n in count(2): yield (a:=a<<2 if (b:=gcd(a,n)) == 1 else a//b) A334840_list = list(islice(A334840_gen(),30)) # Chai Wah Wu, Mar 18 2023
Formula
a(n) = 2^((n mod 2) + A000120(n) + 1), for n >= 2. - Ctibor O. Zizka, Apr 15 2023
a(n) = 2*A001316(n)*(n mod 2 + 1), for n >= 2. - Ctibor O. Zizka, Apr 15 2023
Comments