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A336695
a(n) = A331410(1+sigma(n)), where A331410 is totally additive with a(2) = 0 and a(p) = 1 + a(p+1) for odd primes.
8
0, 0, 2, 0, 1, 2, 2, 0, 1, 3, 2, 4, 3, 4, 4, 0, 3, 2, 2, 3, 3, 4, 4, 2, 0, 3, 3, 4, 1, 5, 3, 0, 2, 4, 2, 2, 3, 2, 4, 3, 3, 3, 4, 5, 3, 5, 2, 6, 4, 2, 5, 4, 4, 4, 5, 4, 4, 3, 2, 4, 3, 3, 4, 0, 5, 6, 3, 1, 3, 6, 5, 2, 5, 4, 6, 3, 3, 4, 4, 5, 2, 1, 5, 6, 5, 4, 4, 4, 3, 4, 5, 4, 4, 6, 4, 4, 4, 3, 4, 5, 3, 2, 4, 5, 4
OFFSET
1,3
FORMULA
a(n) = A331410(1+A000203(n)) = A331410(A088580(n)) = A331410(A332459(n)).
PROG
(PARI)
A331410(n) = { my(f=factor(n)); sum(k=1, #f~, if(2==f[k, 1], 0, f[k, 2]*(1+A331410(f[k, 1]+1)))); };
A336695(n) = A331410(1+sigma(n));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 31 2020
STATUS
approved