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

1,2

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

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; };
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];

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.

Sequence in context: A323400 A323367 A323370 * A353521 A319349 A353520

Adjacent sequences: A323402 A323403 A323404 * A323406 A323407 A323408

Keyword

nonn

Author

Antti Karttunen, Jan 13 2019

Status

approved