A333177 a(n) = Sum_{d|n, gcd(d, n/d) = 1} (-1)^omega(n/d) * prime(d).

2, 1, 3, 5, 9, 7, 15, 17, 21, 17, 29, 27, 39, 25, 33, 51, 57, 37, 65, 55, 53, 47, 81, 67, 95, 59, 101, 85, 107, 41, 125, 129, 103, 79, 123, 123, 155, 95, 123, 145, 177, 75, 189, 157, 165, 115, 209, 167, 225, 131, 171, 193, 239, 147, 217, 229, 199, 161, 275, 147

Offset

1,1

Links

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

Formula

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

Mathematica

a[n_] := Sum[If[GCD[n/d, d] == 1, (-1)^PrimeNu[n/d] 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, (-1)^omega(n/d) * prime(d))); \\ Michel Marcus, Mar 10 2020

Crossrefs

Cf. A000040, A001221, A007444, A076479, A333178.

Sequence in context: A021828 A094341 A255939 * A169912 A316994 A316993

Adjacent sequences: A333174 A333175 A333176 * A333178 A333179 A333180

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 10 2020

Status

approved