A361706 Inverse Moebius transform applied twice to primes.

2, 7, 9, 19, 15, 37, 21, 50, 39, 65, 35, 116, 45, 91, 87, 134, 63, 174, 71, 200, 125, 155, 87, 322, 125, 197, 172, 282, 113, 383, 131, 349, 217, 271, 213, 555, 161, 311, 267, 546, 183, 555, 195, 482, 402, 379, 215, 857, 267, 546, 369, 602, 245, 768, 349, 774, 421, 503, 281, 1204, 287, 561, 582, 875, 425

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

Cf. A000005, A000040, A007429, A007445, A361707.

Sequence in context: A055673 A177737 A336770 * A293645 A293646 A020895

Adjacent sequences: A361703 A361704 A361705 * A361707 A361708 A361709

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 21 2023

Status

approved