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A366381
Lexicographically earliest infinite sequence such that a(i) = a(j) => A336466(i) = A336466(j) and A336467(i) = A336467(j) for all i, j >= 1, where A336466 is fully multiplicative with a(p) = oddpart(p-1) for any prime p and A336467 is fully multiplicative with a(2) = 1 and a(p) = oddpart(p+1) for odd primes p.
2
1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 4, 1, 5, 3, 2, 1, 6, 1, 7, 2, 3, 4, 8, 1, 6, 5, 1, 3, 9, 2, 10, 1, 4, 6, 11, 1, 12, 7, 5, 2, 13, 3, 14, 4, 2, 8, 15, 1, 16, 6, 6, 5, 17, 1, 18, 3, 7, 9, 19, 2, 20, 10, 3, 1, 21, 4, 22, 6, 8, 11, 23, 1, 24, 12, 6, 7, 25, 5, 26, 2, 1, 13, 27, 3, 28, 14, 9, 4, 29, 2, 30, 8, 10, 15, 31, 1, 32
OFFSET
1,5
COMMENTS
Restricted growth sequence transform of the ordered pair [A336466(n), A336467(n)].
For all i, j: A003602(i) = A003602(j) => A366380(i) = A366380(j) => a(i) = a(j).
LINKS
PROG
(PARI)
up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };
A000265(n) = (n>>valuation(n, 2));
A336466(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(f[k, 1]-1)^f[k, 2]); };
A336467(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265(f[k, 1]+1))^f[k, 2])); };
A366381aux(n) = [A336466(n), A336467(n)];
v366381 = rgs_transform(vector(up_to, n, A366381aux(n)));
A366381(n) = v366381[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 12 2023
STATUS
approved