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A369033
LCM-transform of permutation A241916.
4
1, 2, 3, 2, 5, 3, 7, 2, 1, 5, 11, 3, 13, 7, 1, 2, 17, 1, 19, 5, 1, 11, 23, 3, 1, 13, 1, 7, 29, 1, 31, 2, 1, 17, 1, 1, 37, 19, 1, 5, 41, 1, 43, 11, 1, 23, 47, 3, 1, 1, 1, 13, 53, 1, 1, 7, 1, 29, 59, 1, 61, 31, 1, 2, 1, 1, 67, 17, 1, 1, 71, 1, 73, 37, 1, 19, 1, 1, 79, 5, 1, 41, 83, 1, 1, 43, 1, 11, 89, 1, 1, 23, 1, 47
OFFSET
1,2
COMMENTS
See comments in A368900.
LINKS
FORMULA
a(1) = 1, for n > 1, a(n) = lcm {1..A241916(n)} / lcm {1..A241916(n-1)}.
a(n) = A014963(A241916(n)). [A241916 satisfies the property S defined in A368900]
PROG
(PARI)
up_to = 2^16;
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); };
A209229(n) = (n && !bitand(n, n-1));
A241916(n) = if(1==A209229(n), n, my(f = factor(2*n), nbf = #f~, igp = primepi(f[nbf, 1]), g = f); for(i=1, nbf, g[i, 1] = prime(1+igp-primepi(f[i, 1]))); factorback(g)/2); \\ Antti Karttunen, Jan 12 2024
v369033 = LCMtransform(vector(up_to, i, A241916(i)));
A369033(n) = v369033[n];
(PARI)
A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 12 2024
STATUS
approved