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A361706
Inverse Moebius transform applied twice to primes.
2
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
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