A322810 - OEIS

A322810

Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = 0 if n is an odd squarefree number > 1, and f(n) = n for all other numbers.

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 3, 11, 3, 12, 3, 13, 3, 14, 3, 15, 16, 17, 18, 19, 3, 20, 3, 21, 3, 22, 3, 23, 3, 24, 3, 25, 3, 26, 3, 27, 28, 29, 3, 30, 31, 32, 3, 33, 3, 34, 3, 35, 3, 36, 3, 37, 3, 38, 39, 40, 3, 41, 3, 42, 3, 43, 3, 44, 3, 45, 46, 47, 3, 48, 3, 49, 50, 51, 3, 52, 3, 53, 3, 54, 3, 55, 3, 56, 3, 57, 3, 58, 3, 59, 60, 61, 3, 62, 3, 63, 3

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OFFSET

1,2

COMMENTS

For all i, j:

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

a(i) = a(j) => A305980(i) = A305980(j),

a(i) = a(j) => A322808(i) = A322808(j).

LINKS

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

FORMULA

a(1) = 1, a(2) = 2, for n > 2, if n is an odd squarefree number (in A056911), a(n) = 3, otherwise a(n) = running count from 4 onward.

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; };

A322810aux(n) = if((n>1)&&(n%2)&&issquarefree(n), 0, n);

v322810 = rgs_transform(vector(up_to, n, A322810aux(n)));

A322810(n) = v322810[n];

CROSSREFS

Cf. A305801, A305980, A322808.

Cf. A056911 (after the initial 1, gives the positions of 3's in this sequence).

Sequence in context: A331174 A355836 A328470 * A322024 A326203 A355835

Adjacent sequences: A322807 A322808 A322809 * A322811 A322812 A322813

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 27 2018

STATUS

approved