A070288 a(n) = Sum_{d|n} omega(d)*omega(n/d).

0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 6, 0, 2, 2, 3, 0, 6, 0, 6, 2, 2, 0, 10, 1, 2, 2, 6, 0, 12, 0, 4, 2, 2, 2, 14, 0, 2, 2, 10, 0, 12, 0, 6, 6, 2, 0, 14, 1, 6, 2, 6, 0, 10, 2, 10, 2, 2, 0, 26, 0, 2, 6, 5, 2, 12, 0, 6, 2, 12, 0, 22, 0, 2, 6, 6, 2, 12, 0, 14, 3, 2, 0, 26, 2, 2, 2, 10, 0, 26, 2, 6, 2, 2, 2

Offset: 1

Author

Benoit Cloitre, May 12 2002

Keywords

• easy
• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A001221, A062799.

Programs

Mathematica

a[n_] := DivisorSum[n, PrimeNu[#] * PrimeNu[n/#] &]; Array[a, 100] (* Amiram Eldar, May 20 2022 *)

PARI

for(n=1,100,print1(sumdiv(n,d,omega(n/d)*omega(d)),","))

Formula

a(n) = Sum_{prime p|n} A062799(n/p) = Sum_{prime p|n} Sum_{prime q|(n/p)} A000005(n/p/q). - Max Alekseyev, Aug 11 2016