OFFSET
1,1
COMMENTS
a(n) >= prime(n) + 2 for n > 1, with equality iff n is a prime power (A246655). - Robert Israel, Apr 07 2026
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{d|n, gcd(d, n/d) = 1} (-1)^omega(n/d) * a(d) = prime(n).
MAPLE
f:= proc(n) local F, t, D, d;
F:= map(t -> t[1]^t[2], ifactors(n)[2]);
D:= map(convert, combinat:-powerset(F), `*`);
add(ithprime(d), d=D)
end proc:
map(f, [$1..100]); # Robert Israel, Apr 07 2026
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
KEYWORD
nonn,look
AUTHOR
Ilya Gutkovskiy, Mar 10 2020
STATUS
approved
