A353565 Lexicographically earliest infinite sequence such that a(i) = a(j) => A353564(i) = A353564(j), where A353564(n) = Product_{d|n, dA276086(phi(d)).

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

Offset: 1

Author

Antti Karttunen, Apr 27 2022

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of A353564.

For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A051953(i) = A051953(j).

Links

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

Crossrefs

Cf. A000010, A051953, A276086, A353563, A353564.

Cf. also A305800, A318835.

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; };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A353564(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A276086(eulerphi(d)))); m; };
v353565 = rgs_transform(vector(up_to,n,A353564(n)));
A353565(n) = v353565[n];