A335904 Fully additive with a(2) = 0, and a(p) = 1+a(p-1)+a(p+1), for odd primes p.

0, 0, 1, 0, 2, 1, 2, 0, 2, 2, 4, 1, 4, 2, 3, 0, 3, 2, 5, 2, 3, 4, 6, 1, 4, 4, 3, 2, 6, 3, 4, 0, 5, 3, 4, 2, 8, 5, 5, 2, 6, 3, 8, 4, 4, 6, 8, 1, 4, 4, 4, 4, 8, 3, 6, 2, 6, 6, 10, 3, 8, 4, 4, 0, 6, 5, 9, 3, 7, 4, 7, 2, 11, 8, 5, 5, 6, 5, 8, 2, 4, 6, 10, 3, 5, 8, 7, 4, 9, 4, 6, 6, 5, 8, 7, 1, 6, 4, 6, 4, 9, 4, 9, 4, 5

Offset

1,5

Links

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

Formula

Totally additive with a(2) = 0, and for odd primes p, a(p) = 1 + a(p-1) + a(p+1).

a(n) = A336118(n) + A087436(n).

For all n >= 1, a(A335915(n)) = A336118(n).

For all n >= 1, a(n) >= A335884(n) >= A335881(n) >= A335875(n) >= A335885(n).

For all n >= 0, a(3^n) = n.

Prog

(PARI) A335904(n) = { my(f=factor(n)); sum(k=1, #f~, if(2==f[k, 1], 0, f[k, 2]*(1+A335904(f[k, 1]-1)+A335904(f[k, 1]+1)))); };

Crossrefs

Cf. A000244, A052126, A087436, A171462, A335875, A335876, A335881, A335884, A335885, A335905, A335906, A335915, A336118.

Sequence in context: A093321 A302015 A046144 * A144736 A137423 A127471

Adjacent sequences: A335901 A335902 A335903 * A335905 A335906 A335907

Keyword

nonn

Author

Antti Karttunen, Jun 29 2020

Status

approved