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A369060
LCM-transform of Sycamore's D(3) variant of Doudna sequence (A356867).
2
1, 2, 3, 5, 2, 1, 1, 2, 3, 7, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 5, 1, 1, 1, 2, 3, 11, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 2, 3, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,2
COMMENTS
See discussion at A368900.
LINKS
FORMULA
a(n) = lcm {1..A356867(n)} / lcm {1..A356867(n-1)}.
a(n) = A014963(A356867(n)). [This holds because A356867 satisfies the property S explained in A368900]
PROG
(PARI)
up_to = 3^9; \\ Checked up to (3^12)
A356867list(up_to) = { my(v=vector(up_to), met=Map(), h=0, ak); for(i=1, #v, if(1==sumdigits(i, 3), v[i] = i; h = i, ak = v[i-h]; forprime(p=2, , if(3!=p && !mapisdefined(met, p*ak), v[i] = p*ak; break))); mapput(met, v[i], i)); (v); };
v356867 = A356867list(up_to);
A356867(n) = v356867[n];
LCMtransform(v) = { my(len = length(v), b = vector(len), g = vector(len)); b[1] = g[1] = 1; for(n=2, len, g[n] = lcm(g[n-1], v[n]); b[n] = g[n]/g[n-1]); (b); };
v369060 = LCMtransform(v356867);
A369060(n) = v369060[n];
A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 13 2024
STATUS
approved