A323081 -id:A323081 - cp's OEIS frontend

A323080 Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(1)=0, and f(n) = A252463(n) for n > 1.

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

Offset: 1

Antti Karttunen, Jan 03 2019

For all i, j:
  a(i) = a(j) => A252463(i) = A252463(j) => A285727(i) = A285727(j),
  a(i) = a(j) => A320110(i) = A320110(j) => A320111(i) = A320111(j).

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

Cf. A252463, A285727, A320107, A320110, A320111, A322805, A323081.

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; };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A252463(n) = if(!(n%2),n/2,A064989(n));
A323080aux(n) = if(1==n,0,A252463(n));
v323080 = rgs_transform(vector(up_to,n,A323080aux(n)));
A323080(n) = v323080[n];

A323074 Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = -(n mod 4) if n is a prime, and f(n) = A300840(n) for any other number.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jan 04 2019

nonn

For all i, j:

A319704(i) = A319704(j) => a(i) = a(j) => A323082(i) = A323082(j).

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

Cf. A052330, A300840, A319704, A323081, A323082.

up_to = 65539;
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);
A323074aux(n) = if(isprime(n),-(n%4),A300840(n));
v323074 = rgs_transform(vector(up_to,n,A323074aux(n)));
A323074(n) = v323074[n];

cp's OEIS Frontend

A323080 Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(1)=0, and f(n) = A252463(n) for n > 1.

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