A323078 - OEIS

A323078

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 prime, and f(n) = A097246(n) for all other numbers.

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

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OFFSET

1,2

COMMENTS

For all i, j: a(i) = a(j) => A322869(i) = A322869(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; };

A097246(n) = { my(f=factor(n)); prod(i=1, #f~, (nextprime(f[i, 1]+1)^(f[i, 2]\2))*((f[i, 1])^(f[i, 2]%2))); };

A323078aux(n) = if((n>2)&&isprime(n), 0, A097246(n));

v323078 = rgs_transform(vector(up_to, n, A323078aux(n)));

A323078(n) = v323078[n];

CROSSREFS

Cf. A097246, A305801, A322808, A322869.

Sequence in context: A323082 A212356 A322816 * A331301 A002333 A323241

Adjacent sequences: A323075 A323076 A323077 * A323079 A323080 A323081

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 03 2019

STATUS

approved