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

Author

Antti Karttunen, Jun 29 2020

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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)))); };

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.