A325811 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) where f(n) = [A034460(n), A325814(n)] for all other numbers, except f(p) = -1 for odd primes.

1, 2, 3, 2, 3, 4, 3, 2, 5, 6, 3, 7, 3, 8, 9, 2, 3, 10, 3, 11, 12, 13, 3, 14, 15, 16, 17, 18, 3, 19, 3, 2, 20, 21, 22, 23, 3, 24, 25, 26, 3, 27, 3, 28, 29, 30, 3, 31, 32, 33, 34, 35, 3, 36, 37, 38, 39, 40, 3, 41, 3, 42, 25, 2, 43, 44, 3, 45, 46, 47, 3, 48, 3, 49, 50, 51, 52, 53, 3, 54, 32, 55, 3, 56, 57, 58, 59, 60, 3, 61, 62, 63, 64, 65, 66, 67, 3, 68, 69, 70, 3

Offset

1,2

Comments

For all i, j:

A305801(i) = A305801(j) => a(i) = a(j),

A325810(i) = A325810(j) => a(i) = a(j) => A325813(i) = A325813(i).

Links

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

Prog

(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; };
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A034460(n) = (A034448(n) - n);
A048146(n) = (sigma(n)-A034448(n));
A325814(n) = (n-A048146(n));
Aux325811(n) = if(isprime(n)&&(n%2), -(n%2), [A034460(n), A325814(n)]);
v325811 = rgs_transform(vector(up_to, n, Aux325811(n)));
A325811(n) = v325811[n];

Crossrefs

Cf. A034460, A305801, A325810, A325813, A325814.

Sequence in context: A086374 A322591 A332827 * A324380 A123182 A069464

Adjacent sequences: A325808 A325809 A325810 * A325812 A325813 A325814

Keyword

nonn

Author

Antti Karttunen, May 23 2019

Status

approved