A323241 - OEIS

A323241

Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n<=2) = -n, f(n) = 0 if n is an odd number > 1, and f(n) = A300226(n) for even numbers >= 4.

1, 2, 3, 4, 3, 5, 3, 6, 3, 5, 3, 7, 3, 5, 3, 8, 3, 9, 3, 7, 3, 5, 3, 10, 3, 5, 3, 7, 3, 11, 3, 12, 3, 5, 3, 13, 3, 5, 3, 10, 3, 11, 3, 7, 3, 5, 3, 14, 3, 15, 3, 7, 3, 16, 3, 10, 3, 5, 3, 17, 3, 5, 3, 18, 3, 11, 3, 7, 3, 19, 3, 20, 3, 5, 3, 7, 3, 11, 3, 14, 3, 5, 3, 17, 3, 5, 3, 10, 3, 21, 3, 7, 3, 5, 3, 22, 3, 23, 3, 24, 3, 11, 3, 10, 3

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OFFSET

1,2

COMMENTS

For all i, j:

A319701(i) = A319701(j) => a(i) = a(j),

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

a(i) = a(j) => A183063(i) = A183063(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

PROG

(PARI)

up_to = 10000;

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; };

A052126(n) = if(1==n, n, n/vecmax(factor(n)[, 1]));

A319988(n) = ((n>1)&&(factor(n)[omega(n), 2]>1));

A323241aux(n) = if(n<=2, -n, if(n%2, 0, [A052126(n), A319988(n)]));

v323241 = rgs_transform(vector(up_to, n, A323241aux(n)));

A323241(n) = v323241[n];

CROSSREFS

Cf. A007814, A052126, A183063, A300226, A319701, A319988, A323235, A323237, A323238, A323242.

Sequence in context: A323078 A331301 A002333 * A322311 A323237 A323238

Adjacent sequences: A323238 A323239 A323240 * A323242 A323243 A323244

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 07 2019

STATUS

approved