A323237 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = A291756(n) for all n, except f(1) = -1 and for odd numbers n > 1, f(n) = 0.

1, 2, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 3, 10, 3, 11, 3, 12, 3, 13, 3, 14, 3, 15, 3, 16, 3, 17, 3, 18, 3, 19, 3, 20, 3, 21, 3, 22, 3, 15, 3, 23, 3, 24, 3, 25, 3, 26, 3, 27, 3, 28, 3, 29, 3, 30, 3, 31, 3, 32, 3, 33, 3, 34, 3, 35, 3, 36, 3, 37, 3, 38, 3, 39, 3, 36, 3, 40, 3, 41, 3, 27, 3, 42, 3, 43, 3, 44, 3, 45, 3, 46, 3, 47, 3, 48, 3, 49, 3, 50, 3, 51, 3

Offset

1,2

Comments

For all i, j:

A319701(i) = A319701(j) => a(i) = a(j) => A319998(i) = A319998(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] = f[i, 2]-1); factorback(f); };
A173557(n) = my(f=factor(n)[, 1]); prod(k=1, #f, f[k]-1); \\ From A173557
Aux323237(n) = if(1==n, -1, if(n%2, 0, (1/2)*(2 + ((A003557(n)+A173557(n))^2) - A003557(n) - 3*A173557(n))));
v323237 = rgs_transform(vector(up_to, n, Aux323237(n)));
A323237(n) = v323237[n];

Crossrefs

Cf. A003557, A173557, A291756, A295887, A319701, A319998, A322587, A323238, A323241.

Sequence in context: A002333 A323241 A322311 * A323238 A319701 A355833

Adjacent sequences: A323234 A323235 A323236 * A323238 A323239 A323240

Keyword

nonn

Author

Antti Karttunen, Jan 08 2019

Status

approved