A005072 Sum of cubes of primes = 1 mod 3 dividing n.

0, 0, 0, 0, 0, 0, 343, 0, 0, 0, 0, 0, 2197, 343, 0, 0, 0, 0, 6859, 0, 343, 0, 0, 0, 0, 2197, 0, 343, 0, 0, 29791, 0, 0, 0, 343, 0, 50653, 6859, 2197, 0, 0, 343, 79507, 0, 0, 0, 0, 0, 343, 0, 0, 2197, 0, 0, 0, 343, 6859, 0, 0, 0, 226981, 29791, 343, 0, 2197, 0, 300763, 0, 0, 343, 0, 0, 389017, 50653, 0, 6859, 343, 2197, 493039

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A000578, A005070, A005071, A005073.

Programs

Mathematica

f[p_, e_] := If[Mod[p, 3] == 1, p^3, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

PARI

a(n) = my(f=factor(n)); sum(k=1, #f~, if (((p=f[k,1])%3) == 1, p^3)); \\ Michel Marcus, Jul 10 2017

Scheme

(define (A005072 n) (if (= 1 n) 0 (+ (A000578 (if (= 1 (modulo (A020639 n) 3)) (A020639 n) 0)) (A005072 (A028234 n))))) ;; Antti Karttunen, Jul 09 2017

Formula

Additive with a(p^e) = p^3 if p = 1 (mod 3), 0 otherwise.

Extensions

More terms from Antti Karttunen, Jul 09 2017