A334862 a(n) = A334097(n) - A064415(n).

0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 2, 0, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 0, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 3, 1, 1, 1, 2, 2, 2, 1, 2, 3, 2, 1, 3, 2, 2, 2, 1, 1, 3, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 1, 4, 1, 1, 2, 2, 2, 3, 1, 2, 3, 2, 1, 2, 1, 3, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3

Offset

1,9

Comments

Completely additive because A064415 and A334097 are.

Links

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

Formula

a(2) = 0, a(p) = A334097(p+1)-A064415(p-1) for odd primes p, a(m*n) = a(m)+a(n), if m,n > 1.

a(n) = A334097(n) - A064415(n).

a(3^k) = k for all k>= 0.

Prog

(PARI)
A064415(n) = { my(f=factor(n)); sum(k=1, #f~, if(2==f[k, 1], f[k, 2], f[k, 2]*A064415(f[k, 1]-1))); };
A334097(n) = { my(f=factor(n)); sum(k=1, #f~, if(2==f[k, 1], f[k, 2], f[k, 2]*A334097(f[k, 1]+1))); };
A334862(n) = (A334097(n)-A064415(n));
\\ Or alternatively as:
A334862(n) = { my(f=factor(n)); sum(k=1, #f~, if(2==f[k, 1], 0, f[k, 2]*(A334097(f[k, 1]+1)-A064415(f[k, 1]-1)))); };

Crossrefs

Cf. A000079 (positions of zeros), A000244, A064415, A334097, A334861.

Sequence in context: A154338 A087436 A340831 * A329801 A053255 A085856

Adjacent sequences: A334859 A334860 A334861 * A334863 A334864 A334865

Keyword

nonn

Author

Antti Karttunen, May 14 2020

Status

approved