A336460 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A278222(n), A336158(n), A336466(n)], for all i, j >= 1.

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 3, 5, 9, 3, 10, 6, 11, 2, 12, 7, 13, 4, 14, 8, 15, 1, 16, 3, 17, 5, 18, 9, 19, 3, 20, 10, 21, 6, 22, 11, 23, 2, 24, 12, 25, 7, 26, 13, 27, 4, 28, 14, 29, 8, 30, 15, 31, 1, 32, 16, 33, 3, 34, 17, 35, 5, 18, 18, 22, 9, 36, 19, 37, 3, 38, 20, 39, 10, 40, 21, 41, 6, 42, 22, 43, 11, 44, 23, 45, 2, 7, 24, 46, 12, 47, 25, 48, 7, 49

Offset

1,3

Comments

Restricted growth sequence transform of the ordered triple [A278222(n), A336158(n), A336466(n)].

For all i, j:

A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j),

a(i) = a(j) => A336159(i) = A336159(j),

a(i) = a(j) => A336470(i) = A336470(j) => A336471(i) = A336471(j),

a(i) = a(j) => A336472(i) = A336472(j),

a(i) = a(j) => A336473(i) = A336473(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));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
A336158(n) = A046523(A000265(n));
A336466(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265(f[k, 1]-1))^f[k, 2])); };
Aux336460(n) = [A278222(n), A336158(n), A336466(n)];
v336460 = rgs_transform(vector(up_to, n, Aux336460(n)));
A336460(n) = v336460[n];

Crossrefs

Cf. A278222, A336158, A336466.

Cf. A003602, A324400, A336159, A336470, A336471, A336472, A336473.

Sequence in context: A365395 A366792 A336933 * A108712 A351037 A351461

Adjacent sequences: A336457 A336458 A336459 * A336461 A336462 A336463

Keyword

nonn

Author

Antti Karttunen, Jul 24 2020

Status

approved