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

1,2

Links

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

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

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

Sequence in context: A319701 A355833 A319339 * A322805 A322809 A366384

Adjacent sequences: A322804 A322805 A322806 * A322808 A322809 A322810

Keyword

nonn

Author

Antti Karttunen, Dec 26 2018

Status

approved