A323078 Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = 0 if n is an odd prime, and f(n) = A097246(n) for all other numbers.

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

Offset: 1

Author

Antti Karttunen, Jan 03 2019

Keywords

• nonn

Comments

For all i, j: a(i) = a(j) => A322869(i) = A322869(j).

Links

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

Crossrefs

Cf. A097246, A305801, A322808, A322869.

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; };
A097246(n) = { my(f=factor(n)); prod(i=1, #f~, (nextprime(f[i,1]+1)^(f[i,2]\2))*((f[i,1])^(f[i,2]%2))); };
A323078aux(n) = if((n>2)&&isprime(n),0,A097246(n));
v323078 = rgs_transform(vector(up_to,n,A323078aux(n)));
A323078(n) = v323078[n];