OFFSET
1,6
COMMENTS
Dirichlet convolution of A001222 with itself.
LINKS
FORMULA
EXAMPLE
24 has 8 divisors, namely 1, 2, 3, 4, 6, 8, 12, 24, and four prime factors counted with multiplicity. The divisors have 0, 1, 1, 2, 2, 3, 3, 4 divisors respectively. So a(24) = 0 * (4 - 0) + 1 * (4 - 1) + 1 * (4 - 1) + 2 * (4 - 2) + 2 * (4 - 2) + 3 * (4 - 3) + 4 * (4 - 4) = 0 + 3 + 3 + 4 + 4 + 3 + 3 + 0 = 20. - David A. Corneth, Jan 12 2019
MAPLE
f:= proc(n) local F, G, t, x;
F:= map(t -> t[2], ifactors(n)[2]);
G:= unapply(normal(mul((1-x^(t+1))/(1-x), t = F)), x);
(convert(F, `+`)-1)*D(G)(1) - (D@@2)(G)(1);
end proc:
map(f, [$1..100]); # Robert Israel, Jan 17 2019
MATHEMATICA
Table[Sum[PrimeOmega[d] PrimeOmega[n/d], {d, Divisors[n]}], {n, 95}]
PROG
(PARI) a(n) = sumdiv(n, d, bigomega(d)*bigomega(n/d)); \\ Michel Marcus, Aug 25 2018
(PARI) a(n) = bn = bigomega(n); sumdiv(n, d, bd = bigomega(d); bd * (bn - bd)) \\ David A. Corneth, Jan 12 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 24 2018
STATUS
approved