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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.
2
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
1,2
COMMENTS
For all i, j:
A319704(i) = A319704(j) => a(i) = a(j) => A323082(i) = A323082(j).
LINKS
PROG
(PARI)
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];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 04 2019
STATUS
approved