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.

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

Antti Karttunen, Table of n, a(n) for n = 1..65537

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
A336158(n) = A046523(A000265(n));
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

Cf. A000265, A003602, A335880, A336158, A336466, A336467, A336470, A336390, A366381.

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

Adjacent sequences: A366377 A366378 A366379 * A366381 A366382 A366383

Keyword

nonn

Author

Antti Karttunen, Oct 12 2023

Status

approved