A333178 a(n) = Sum_{d|n, gcd(d, n/d) = 1} prime(d).

2, 5, 7, 9, 13, 23, 19, 21, 25, 45, 33, 51, 43, 65, 65, 55, 61, 89, 69, 91, 97, 115, 85, 115, 99, 147, 105, 133, 111, 223, 129, 133, 175, 203, 179, 183, 159, 235, 215, 205, 181, 337, 193, 233, 233, 287, 213, 283, 229, 331, 299, 289, 243, 359, 301, 301, 343, 385, 279, 461

Offset

1,1

Links

Table of n, a(n) for n=1..60.

Formula

Sum_{d|n, gcd(d, n/d) = 1} (-1)^omega(n/d) * a(d) = prime(n).

Mathematica

a[n_] := Sum[If[GCD[n/d, d] == 1, Prime[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 60}]

Prog

(PARI) a(n) = sumdiv(n, d, if (gcd(d, n/d) ==1, prime(d))); \\ Michel Marcus, Mar 10 2020

Crossrefs

Cf. A000040, A001221, A007445, A076479, A333177.

Sequence in context: A151716 A175072 A115863 * A169867 A287363 A253275

Adjacent sequences: A333175 A333176 A333177 * A333179 A333180 A333181

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 10 2020

Status

approved