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A322807
Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = -1 if n is an odd prime, and f(n) = A285330(n) for all other numbers.
7
1, 2, 3, 4, 3, 5, 3, 6, 5, 7, 3, 8, 3, 9, 8, 10, 3, 11, 3, 12, 12, 13, 3, 14, 7, 15, 9, 16, 3, 17, 3, 18, 14, 19, 11, 20, 3, 21, 22, 23, 3, 24, 3, 25, 26, 27, 3, 28, 17, 29, 30, 31, 3, 32, 23, 33, 34, 35, 3, 36, 3, 37, 38, 39, 28, 40, 3, 22, 41, 42, 3, 43, 3, 44, 45, 46, 20, 47, 3, 48, 49, 50, 3, 51, 52, 53, 54, 55, 3, 56, 29, 57, 58, 59, 60, 61, 3, 62, 15
OFFSET
1,2
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; };
A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947
A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ From A048675
A285328(n) = { my(r); if((n > 1 && !bitand(n, (n-1))), (n/2), r=A007947(n); if(r==n, 1, n = n-r; while(A007947(n) <> r, n = n-r); n)); };
A285330(n) = if(issquarefree(n), A048675(n), A285328(n));
A322807aux(n) = if((n%2)&&isprime(n), -1, A285330(n));
v322807 = rgs_transform(vector(up_to, n, A322807aux(n)));
A322807(n) = v322807[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 26 2018
STATUS
approved