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A365467
Lexicographically earliest infinite sequence such that a(i) = a(j) => A336467(i) = A336467(j) and A336467(A163511(i)) = A336467(A163511(j)) for all i, j >= 1, where A336467 is fully multiplicative with a(2) = 1 and a(p) = oddpart(p+1) for odd primes p.
3
1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 4, 1, 5, 3, 2, 1, 6, 1, 7, 2, 8, 4, 2, 1, 9, 5, 3, 3, 10, 2, 3, 1, 2, 6, 11, 1, 12, 7, 13, 2, 14, 8, 15, 4, 2, 2, 4, 1, 3, 9, 16, 5, 17, 3, 9, 3, 18, 10, 19, 2, 20, 3, 21, 1, 22, 2, 23, 6, 11, 11, 6, 1, 24, 12, 9, 7, 2, 13, 7, 2, 8, 14, 14, 8, 17, 15, 19, 4, 25, 2, 26, 2, 8, 4, 27, 1, 28, 3
OFFSET
1,5
COMMENTS
Restricted growth sequence transform of the ordered pair [A336467(n), A365427(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));
A336467(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265(f[k, 1]+1))^f[k, 2])); };
A365467aux(n) = [A336467(n), A336467(A163511(n))];
v365467 = rgs_transform(vector(up_to, n, A365467aux(n)));
A365467(n) = v365467[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 04 2023
STATUS
approved