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A334862
a(n) = A334097(n) - A064415(n).
3
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 14 2020
STATUS
approved