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A365466
Lexicographically earliest infinite sequence such that a(i) = a(j) => A336466(i) = A336466(j) and A336466(A163511(i)) = A336466(A163511(j)) for all i, j >= 1, where A336466 is fully multiplicative with a(p) = oddpart(p-1) for any prime p.
3
1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 2, 4, 1, 1, 1, 5, 1, 2, 3, 6, 1, 1, 2, 4, 2, 7, 4, 8, 1, 3, 1, 2, 1, 5, 5, 9, 1, 3, 2, 10, 3, 11, 6, 12, 1, 5, 1, 4, 2, 13, 4, 14, 2, 15, 7, 16, 4, 8, 8, 17, 1, 2, 3, 18, 1, 19, 2, 20, 1, 5, 5, 21, 5, 22, 9, 23, 1, 1, 3, 24, 2, 11, 10, 25, 3, 6, 11, 26, 6, 27, 12, 28, 1, 2, 5
OFFSET
1,7
COMMENTS
Restricted growth sequence transform of the ordered pair [A336466(n), A365426(n)].
For all i, j: A003602(i) = A003602(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));
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A336466(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(f[k, 1]-1)^f[k, 2]); };
A365466aux(n) = [A336466(n), A336466(A163511(n))];
v365466 = rgs_transform(vector(up_to, n, A365466aux(n)));
A365466(n) = v365466[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 04 2023
STATUS
approved