A323366 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => A000035(i) = A000035(j) and A003557(i) = A003557(j) and A173557(i) = A173557(j).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 13, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 34, 38, 39, 25, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 39, 52, 36, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 56, 65, 72, 73, 74, 75, 76, 49, 77, 78, 79, 80, 81, 82, 68, 83, 56, 84, 68, 85, 86, 87, 88, 89, 90, 91, 92, 93, 60

Offset: 1

Author

Antti Karttunen, Jan 12 2019

Keywords

• nonn

Comments

For all i, j:

a(i) = a(j) => A007814(i) = A007814(j),

a(i) = a(j) => A295887(i) = A295887(j),

a(i) = a(j) => A323237(i) = A323237(j).

Links

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

Crossrefs

Cf. A000035, A003557, A007814, A173557, A291756, A295887, A323237, A323367.

Cf. also A323368.

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] = f[i, 2]-1); factorback(f); };
A173557(n) = my(f=factor(n)[, 1]); prod(k=1, #f, f[k]-1); \\ From A173557
v323366 = rgs_transform(vector(up_to, n, [(n%2), A003557(n), A173557(n)]));
A323366(n) = v323366[n];