A318995 Totally additive with a(prime(n)) = n - 1.

0, 0, 1, 0, 2, 1, 3, 0, 2, 2, 4, 1, 5, 3, 3, 0, 6, 2, 7, 2, 4, 4, 8, 1, 4, 5, 3, 3, 9, 3, 10, 0, 5, 6, 5, 2, 11, 7, 6, 2, 12, 4, 13, 4, 4, 8, 14, 1, 6, 4, 7, 5, 15, 3, 6, 3, 8, 9, 16, 3, 17, 10, 5, 0, 7, 5, 18, 6, 9, 5, 19, 2, 20, 11, 5, 7, 7, 6, 21, 2, 4, 12

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, A318994.

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,200}]

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