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

1,7

Links

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

Formula

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A000578, A005070, A005071, A005073.

Sequence in context: A023909 A035844 A028681 * A112821 A045130 A045269

Adjacent sequences: A005069 A005070 A005071 * A005073 A005074 A005075

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 09 2017

Status

approved