A332826 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A332824(i)) = A046523(A332824(j)) for all i, j.

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

Offset: 1

Author

Antti Karttunen, Feb 25 2020

Keywords

• nonn

Links

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

Crossrefs

Cf. A000010, A019565, A046523, A332824, A332827.

Cf. A019434 (positions of 3's).

Cf. also 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; };
A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
A332824(n) = { my(m=1); fordiv(n,d,m *= A019565(eulerphi(d))); (m); };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
v332826 = rgs_transform(vector(up_to,n,A046523(A332824(n))));
A332826(n) = v332826[n];