A323371 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = A295886(n) for all other numbers, except f(n) = 0 for odd primes.

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

Offset: 1

Author

Antti Karttunen, Jan 13 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of function f, defined as f(n) = 0 when n is an odd prime, and f(n) = [A003557(n), A023900(n)] for all other numbers.

For all i, j:

A323370(i) = A323370(j) => a(i) = a(j),

A323405(i) = A323405(j) => a(i) = a(j),

a(i) = a(j) => A092248(i) = A092248(j),

a(i) = a(j) => A319340(i) = A319340(j),

a(i) = a(j) => A322587(i) = A322587(j).

Links

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

Crossrefs

Cf. A003557, A023900, A092248, A295886, A305801, A319340, A322587, A323370, A323405.

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; };
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = max(0,f[i, 2]-1)); factorback(f); };
A023900(n) = sumdivmult(n, d, d*moebius(d)); \\ From A023900
Aux323371(n) = if((n>2)&&isprime(n),0,[A003557(n), A023900(n)]);
v323371 = rgs_transform(vector(up_to, n, Aux323371(n)));
A323371(n) = v323371[n];