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A366380
Lexicographically earliest infinite sequence such that a(i) = a(j) => A336158(i) = A336158(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, and A336158(n) gives the prime signature of the odd part of n.
2
1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 20, 3, 21, 11, 22, 6, 23, 12, 24, 2, 25, 13, 26, 7, 27, 14, 28, 4, 29, 15, 30, 8, 31, 16, 32, 1, 33, 17, 34, 9, 35, 18, 36, 5, 37, 19, 38, 10, 39, 20, 40, 3, 41, 21, 42, 11, 43, 22, 44, 6, 45, 23, 46, 12, 47, 24, 48, 2, 49, 25, 50
OFFSET
1,3
COMMENTS
Restricted growth sequence transform of the triplet [A336158(n), A336466(n), A336467(n)].
For all i, j >= 1:
A003602(i) = A003602(j) => a(i) = a(j),
a(i) = a(j) => A366381(i) = A366381(j),
a(i) = a(j) => A335880(i) = A335880(j),
a(i) = a(j) => A336390(i) = A336390(j),
a(i) = a(j) => A336470(i) = A336470(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));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
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])); };
A366380aux(n) = [A336158(n), A336466(n), A336467(n)];
v366380 = rgs_transform(vector(up_to, n, A366380aux(n)));
A366380(n) = v366380[n];
CROSSREFS
Differs from A003602 and A351090 for the first time at n=153, where a(153) = 38, while A003602(153) = A351090(153) = 77.
Differs from A365388 for the first time at n=99, where a(99) = 50, while A365388(99) = 41.
Sequence in context: A351090 A366893 A365388 * A265650 A181733 A049773
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 12 2023
STATUS
approved