A365392 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 1, where f(n) = [A336158(n), A364255(n), A365425(n)].

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 10, 5, 21, 22, 23, 24, 25, 12, 26, 7, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 19, 39, 10, 5, 40, 41, 42, 43, 44, 45, 46, 47, 48, 20, 23, 12, 49, 12, 13, 50, 51, 52, 53, 54, 55, 56, 57, 16, 58, 59, 60, 61, 62, 63, 64, 18, 65, 66, 67, 36

Offset: 1

Author

Antti Karttunen, Sep 04 2023

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of triplet [A336158(n), A364255(n), A365425(n)].

For all i, j >= 1:

a(i) = a(j) => A286531(i) = A286531(j),

a(i) = a(j) => A305891(i) = A305891(j),

a(i) = a(j) => A365391(i) = A365391(j),

a(i) = a(j) => A365421(i) = A365421(j).

Links

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

Crossrefs

Cf. A000265, A046523, A163511, A286531, A305891, A336158, A364255, A365425, A365391, A365421.

Programs

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
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));
A364255(n) = gcd(n, A163511(n));
A365392aux(n) = [A364255(n), A046523(A000265(n)), A046523(A000265(A163511(n)))];
v365392 = rgs_transform(vector(up_to,n,A365392aux(n)));
A365392(n) = v365392[n];