A005074 Sum of primes = 2 mod 3 dividing n.

0, 2, 0, 2, 5, 2, 0, 2, 0, 7, 11, 2, 0, 2, 5, 2, 17, 2, 0, 7, 0, 13, 23, 2, 5, 2, 0, 2, 29, 7, 0, 2, 11, 19, 5, 2, 0, 2, 0, 7, 41, 2, 0, 13, 5, 25, 47, 2, 0, 7, 17, 2, 53, 2, 16, 2, 0, 31, 59, 7, 0, 2, 0, 2, 5, 13, 0, 19, 23, 7, 71, 2, 0, 2, 5, 2, 11, 2, 0, 7, 0, 43, 83, 2, 22, 2, 29, 13, 89, 7, 0, 25, 0, 49, 5

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

Additive with a(p^e) = p if p = 2 (mod 3), 0 otherwise.

a(n) = A008472(n) - A005070(n) - 3*A079978(n). - Antti Karttunen, Jul 10 2017

Mathematica

Array[DivisorSum[#, # &, And[PrimeQ@ #, Mod[#, 3] == 2] &] &, 95] (* Michael De Vlieger, Jul 11 2017 *)
f[p_, e_] := If[Mod[p, 3] == 2, p, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

Prog

(Scheme) (define (A005074 n) (if (= 1 n) 0 (+ (if (= 2 (modulo (A020639 n) 3)) (A020639 n) 0) (A005074 (A028234 n))))) ;; Antti Karttunen, Jul 10 2017
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (((p=f[k, 1])%3) == 2, p)); \\ Michel Marcus, Jul 11 2017

Crossrefs

Cf. A005070, A005075, A005076, A005077, A005090, A008472, A079978.

Sequence in context: A209701 A158855 A344908 * A161564 A078182 A363803

Adjacent sequences: A005071 A005072 A005073 * A005075 A005076 A005077

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 10 2017

Status

approved