A322816 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = A048675(n) for all other numbers, except f(n) = -1 if n is an odd prime.

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

Offset: 1

Author

Antti Karttunen, Dec 27 2018

Keywords

• nonn

Comments

For all i, j > 1:

A323078(i) = A323078(j) => a(i) = a(j),

a(i) = a(j) => A322812(i) = A322812(j),

a(i) = a(j) => A322869(i) = A322869(j).

Links

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

Crossrefs

Cf. A048675, A305801, A322812, A322815, A322869, A323078.

Programs

PARI

up_to = 4096;
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; };
A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ From A048675
A322816aux(n) = if((n>2)&&isprime(n),-1,A048675(n));
v322816 = rgs_transform(vector(up_to,n,A322816aux(n)));
A322816(n) = v322816[n];