A336162 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A335915(i) = A335915(j), for all i, j >= 1.

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, 13, 5, 18, 10, 19, 3, 20, 11, 21, 6, 22, 12, 23, 2, 13, 13, 24, 7, 25, 14, 26, 4, 27, 15, 28, 8, 29, 16, 30, 1, 31, 17, 32, 9, 33, 13, 34, 5, 35, 18, 36, 10, 37, 19, 38, 3, 39, 20, 40, 11, 41, 21, 42, 6, 43, 22, 44, 12, 45, 23, 46, 2, 47, 13, 48, 13, 49, 24, 50, 7, 36

Offset

1,3

Comments

Restricted growth sequence transform of the ordered pair [A278222(n), A335915(n)].

For all i, j: A324400(i) = A324400(j) => a(i) = a(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));
A335915(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265(f[k, 1]-1)*A000265(f[k, 1]+1))^f[k, 2])); };
Aux336162(n) = [A278222(n), A335915(n)];
v336162 = rgs_transform(vector(up_to, n, Aux336162(n)));
A336162(n) = v336162[n];

Crossrefs

Cf. A000265, A005940, A046523, A278222, A335915.

Cf. also A286622, A324400, A336155, A336159, A336160.

Sequence in context: A366886 A336392 A336935 * A351035 A351036 A351040

Adjacent sequences: A336159 A336160 A336161 * A336163 A336164 A336165

Keyword

nonn

Author

Antti Karttunen, Jul 11 2020

Status

approved