A322811 a(1) = 0; for n > 1, a(n) = A001221(A285330(n)).

0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 3, 2, 1, 2, 2, 2, 3, 2, 1, 3, 1, 2, 2, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 3, 2, 2, 2, 2, 1, 3, 2, 2, 3, 3, 3, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2

Offset: 1

Author

Antti Karttunen, Dec 27 2018

Keywords

• nonn

Comments

For all i, j:

A322806(i) = A322806(j) => a(i) = a(j),

A322807(i) = A322807(j) => a(i) = a(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A048675, A285330, A322806, A322807, A322812.

Programs

PARI

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));
A322811(n) = if(1==n,0,omega(A285330(n)));

Formula

a(1) = 0; for n > 1, a(n) = A001221(A285330(n)).

If n > 1 is squarefree, a(n) = A322812(n) = A001221(A048675(n)), otherwise a(n) = A001221(A285328(n)) = A001221(n).