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.

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

Author

Antti Karttunen, Dec 26 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A048675, A285328, A285330, A285332, A322806.

Programs

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];