OFFSET
1,1
COMMENTS
Dirichlet convolution of primes with the number of divisors function.
LINKS
Winston de Greef, Table of n, a(n) for n = 1..10000
N. J. A. Sloane, Transforms
FORMULA
G.f.: Sum_{i>=1} Sum_{j>=1} prime(i) * x^(i*j) / (1 - x^(i*j)).
a(n) = Sum_{d|n} A000005(n/d) * prime(d).
MAPLE
a:= (proc(p) proc(n) uses numtheory;
add(p(d), d=divisors(n))
end end@@2)(ithprime):
seq(a(n), n=1..100); # Alois P. Heinz, Mar 23 2023
MATHEMATICA
Table[Sum[DivisorSigma[0, n/d] Prime[d], {d, Divisors[n]}], {n, 1, 65}]
PROG
(PARI) a(n) = sumdiv(n, d, numdiv(n/d)*prime(d)); \\ Michel Marcus, Mar 23 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 21 2023
STATUS
approved