A323082 - OEIS

A323082

Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = -(n mod 2) if n is a prime, and f(n) = A300840(n) for any other number.

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

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OFFSET

1,2

COMMENTS

For all i, j: A323074(i) = A323074(j) => a(i) = a(j).

Like the related A322822 also this filter sequence satisfies the following two implications, for all i, j >= 1:

a(i) = a(j) => A322356(i) = A322356(j),

a(i) = a(j) => A290105(i) = A290105(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65539

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; };

ispow2(n) = (n && !bitand(n, n-1));

A302777(n) = ispow2(isprimepower(n));

A050376list(up_to) = { my(v=vector(up_to), i=0); for(n=1, oo, if(A302777(n), i++; v[i] = n); if(i == up_to, return(v))); };

v050376 = A050376list(up_to);

A050376(n) = v050376[n];

A052330(n) = { my(p=1, i=1); while(n>0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); };

A052331(n) = { my(s=0, e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&A302777(n/d), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };

A300840(n) = A052330(A052331(n)>>1);

A323082aux(n) = if(isprime(n), -(n%2), A300840(n));

v323082 = rgs_transform(vector(up_to, n, A323082aux(n)));

A323082(n) = v323082[n];

CROSSREFS

Cf. A052330, A300840, A305801, A322822, A323074.

Cf. also A290105, A322356.

Sequence in context: A324399 A325382 A324401 * A212356 A322816 A323078

Adjacent sequences: A323079 A323080 A323081 * A323083 A323084 A323085

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 04 2019

STATUS

approved