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A322805
Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(1)=0, f(2)=1, f(n)=-1 for odd primes, and f(n) = A252463(n) for any other number.
6
1, 2, 3, 4, 3, 5, 3, 6, 6, 7, 3, 8, 3, 9, 8, 10, 3, 11, 3, 12, 12, 13, 3, 14, 11, 15, 10, 16, 3, 17, 3, 18, 16, 19, 17, 20, 3, 21, 22, 23, 3, 24, 3, 22, 14, 25, 3, 26, 27, 27, 28, 28, 3, 29, 24, 30, 31, 32, 3, 33, 3, 34, 23, 35, 36, 36, 3, 31, 37, 38, 3, 39, 3, 40, 20, 37, 38, 41, 3, 42, 18, 43, 3, 44, 41, 45, 46, 47, 3, 48, 49, 46, 50, 51, 52, 53, 3, 54, 30, 55, 3, 52, 3, 56, 33
OFFSET
1,2
COMMENTS
For all i, j:
a(i) = a(j) => A319694(i) = A319694(j),
a(i) = a(j) => A319699(i) = A319699(j),
a(i) = a(j) => A319700(i) = A319700(j),
a(i) = a(j) => A319703(i) = A319703(j),
a(i) = a(j) => A319989(i) = A319989(j),
a(i) = a(j) => A320110(i) = A320110(j) => A320111(i) = A320111(j).
LINKS
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; };
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));
A322805aux(n) = if(n<=2, n-1, if(isprime(n), -1, A252463(n)));
v322805 = rgs_transform(vector(up_to, n, A322805aux(n)));
A322805(n) = v322805[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 26 2018
STATUS
approved