A318994 Totally additive with a(prime(n)) = n + 1.

0, 2, 3, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 8, 8, 8, 10, 9, 8, 9, 9, 9, 11, 9, 12, 10, 9, 10, 9, 10, 13, 11, 10, 10, 14, 10, 15, 10, 10, 12, 16, 11, 10, 10, 11, 11, 17, 11, 10, 11, 12, 13, 18, 11, 19, 14, 11, 12, 11, 11, 20, 12, 13, 11, 21, 12, 22

Offset: 1

Author

Gus Wiseman, Sep 07 2018

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001222, A003963, A056239, A275024, A299757, A302242, A302243, A318995.

Programs

Maple

a:= n-> add((1+numtheory[pi](i[1]))*i[2], i=ifactors(n)[2]):
seq(a(n), n=1..100);  # Alois P. Heinz, Sep 07 2018

Mathematica

Table[Cases[If[n==1,{},FactorInteger[n]],{p_,k_}:>(PrimePi[p]+1)*k]//Total,{n,100}]

PARI

a(n)={my(f=factor(n)); sum(i=1, #f~, my([p,e]=f[i,]); (primepi(p)+1)*e)} \\ Andrew Howroyd, Sep 07 2018