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

1,2

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

Prog

(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];

Crossrefs

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

Sequence in context: A324401 A323082 A212356 * A323078 A331301 A002333

Adjacent sequences: A322813 A322814 A322815 * A322817 A322818 A322819

Keyword

nonn

Author

Antti Karttunen, Dec 27 2018

Status

approved