A005076 Sum of cubes of primes = 2 mod 3 dividing n.

0, 8, 0, 8, 125, 8, 0, 8, 0, 133, 1331, 8, 0, 8, 125, 8, 4913, 8, 0, 133, 0, 1339, 12167, 8, 125, 8, 0, 8, 24389, 133, 0, 8, 1331, 4921, 125, 8, 0, 8, 0, 133, 68921, 8, 0, 1339, 125, 12175, 103823, 8, 0, 133, 4913, 8, 148877, 8, 1456, 8, 0, 24397, 205379, 133, 0, 8, 0, 8, 125, 1339, 0, 4921, 12167, 133, 357911

Offset

1,2

Links

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

Formula

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

a(n) = A005064(n) - A005072(n) - 27*A079978(n). - Antti Karttunen, Jul 10 2017

Mathematica

Array[DivisorSum[#, #^3 &, And[PrimeQ@ #, Mod[#, 3] == 2] &] &, 71] (* Michael De Vlieger, Jul 11 2017 *)
f[p_, e_] := If[Mod[p, 3] == 2, p^3, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

Prog

(Scheme) (define (A005076 n) (if (= 1 n) 0 (+ (A000578 (if (= 2 (modulo (A020639 n) 3)) (A020639 n) 0)) (A005076 (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^3)); \\ Michel Marcus, Jul 11 2017

Crossrefs

Cf. A000578, A005064, A005072, A005074, A005075, A005077, A008472, A079978.

Sequence in context: A341485 A076350 A197617 * A296182 A019863 A350747

Adjacent sequences: A005073 A005074 A005075 * A005077 A005078 A005079

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 10 2017

Status

approved