A323405 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = [A003557(n), A023900(n), A063994(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, 19, 20, 21, 3, 22, 3, 23, 24, 25, 26, 27, 3, 28, 26, 29, 3, 30, 3, 31, 32, 33, 3, 34, 35, 36, 37, 38, 3, 39, 40, 41, 42, 43, 3, 44, 3, 45, 46, 47, 48, 49, 3, 50, 51, 52, 3, 53, 3, 54, 55, 56, 57, 58, 3, 59, 60, 61, 3, 62, 63, 64, 65, 66, 3, 67, 68, 69, 57, 70, 71, 72, 3, 73, 74, 75, 3

Offset: 1

Author

Antti Karttunen, Jan 13 2019

Keywords

• nonn

Comments

For all i, j:

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

a(i) = a(j) => A323371(i) = A323371(j),

a(i) = a(j) => A247074(i) = A247074(j).

Links

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

Crossrefs

Cf. A000010, A003557, A023900, A063994, A247074, A305801, A323371, A323404.

Differs from A323370 for the first time at n=78, where a(78) = 58, while A323370(78) = 52.

Cf. also A323374.

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
A063994(n) = { my(f=factor(n)[, 1]); prod(i=1, #f, gcd(f[i]-1, n-1)); }; \\ From A063994
Aux323405(n) = if((n>2)&&isprime(n),0,[A003557(n), A023900(n), A063994(n)]);
v323405 = rgs_transform(vector(up_to, n, Aux323405(n)));
A323405(n) = v323405[n];