A323371 - OEIS

A323371

Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = A295886(n) for all other numbers, except f(n) = 0 for odd primes.

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 18, 15, 19, 20, 3, 21, 3, 22, 23, 24, 25, 26, 3, 27, 25, 28, 3, 29, 3, 30, 31, 32, 3, 33, 34, 35, 36, 37, 3, 38, 39, 40, 41, 42, 3, 43, 3, 44, 45, 46, 47, 48, 3, 49, 50, 51, 3, 52, 3, 41, 53, 54, 55, 51, 3, 56, 57, 39, 3, 58, 59, 60, 61, 62, 3, 63, 64, 65, 55, 66, 64, 67, 3, 68, 69

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OFFSET

1,2

COMMENTS

Restricted growth sequence transform of function f, defined as f(n) = 0 when n is an odd prime, and f(n) = [A003557(n), A023900(n)] for all other numbers.

For all i, j:

A323370(i) = A323370(j) => a(i) = a(j),

A323405(i) = A323405(j) => a(i) = a(j),

a(i) = a(j) => A092248(i) = A092248(j),

a(i) = a(j) => A319340(i) = A319340(j),

a(i) = a(j) => A322587(i) = A322587(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] = max(0, f[i, 2]-1)); factorback(f); };

A023900(n) = sumdivmult(n, d, d*moebius(d)); \\ From A023900

Aux323371(n) = if((n>2)&&isprime(n), 0, [A003557(n), A023900(n)]);

v323371 = rgs_transform(vector(up_to, n, Aux323371(n)));

A323371(n) = v323371[n];

CROSSREFS

Cf. A003557, A023900, A092248, A295886, A305801, A319340, A322587, A323370, A323405.

Sequence in context: A318500 A325384 A353522 * A369447 A319346 A323369

Adjacent sequences: A323368 A323369 A323370 * A323372 A323373 A323374

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 13 2019

STATUS

approved