A005080 Sum of cubes of primes = 1 mod 4 dividing n.

0, 0, 0, 0, 125, 0, 0, 0, 0, 125, 0, 0, 2197, 0, 125, 0, 4913, 0, 0, 125, 0, 0, 0, 0, 125, 2197, 0, 0, 24389, 125, 0, 0, 0, 4913, 125, 0, 50653, 0, 2197, 125, 68921, 0, 0, 0, 125, 0, 0, 0, 0, 125, 4913, 2197, 148877, 0, 125, 0, 0, 24389, 0, 125, 226981, 0, 0, 0, 2322, 0, 0, 4913, 0, 125, 0, 0, 389017, 50653, 125

Offset

1,5

Links

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

Formula

Additive with a(p^e) = p^3 if p = 1 (mod 4), 0 otherwise.

a(n) = A005064(n) - A005084(n) - 8*A059841(n). - Antti Karttunen, Jul 11 2017

Mathematica

Array[DivisorSum[#, #^3 &, And[PrimeQ@ #, Mod[#, 4] == 1] &] &, 75] (* Michael De Vlieger, Jul 11 2017 *)
f[p_, e_] := If[Mod[p, 4] == 1, p^3, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

Prog

(Scheme) (define (A005080 n) (if (= 1 n) 0 (+ (if (= 1 (modulo (A020639 n) 4)) (A000578 (A020639 n)) 0) (A005080 (A028234 n))))) ;; Antti Karttunen, Jul 11 2017
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (((p=f[k, 1])%4) == 1, p^3)); \\ Michel Marcus, Jul 11 2017

Crossrefs

Cf. A000578, A005064, A005078, A005079, A005081, A005084, A059841.

Sequence in context: A146553 A009805 A227393 * A174733 A100579 A298062

Adjacent sequences: A005077 A005078 A005079 * A005081 A005082 A005083

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 11 2017

Status

approved