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
Offset: 1
Keywords
Links
- Antti Karttunen, Table of n, a(n) for n = 1..65539
Programs
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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];
Comments