A005073 Sum of 4th powers of primes = 1 mod 3 dividing n.

0, 0, 0, 0, 0, 0, 2401, 0, 0, 0, 0, 0, 28561, 2401, 0, 0, 0, 0, 130321, 0, 2401, 0, 0, 0, 0, 28561, 0, 2401, 0, 0, 923521, 0, 0, 0, 2401, 0, 1874161, 130321, 28561, 0, 0, 2401, 3418801, 0, 0, 0, 0, 0, 2401, 0, 0, 28561, 0, 0, 0, 2401, 130321, 0, 0, 0, 13845841, 923521, 2401, 0, 28561, 0, 20151121, 0, 0, 2401, 0, 0, 28398241, 1874161

Offset

1,7

Links

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

Formula

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

Mathematica

f[p_, e_] := If[Mod[p, 3] == 1, p^4, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

Prog

(Scheme) (define (A005073 n) (if (= 1 n) 0 (+ (A000583 (if (= 1 (modulo (A020639 n) 3)) (A020639 n) 0)) (A005073 (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^4)); \\ Michel Marcus, Jul 10 2017

Crossrefs

Cf. A000583, A005070, A005071, A005072.

Sequence in context: A235414 A235259 A321638 * A176767 A018865 A186488

Adjacent sequences: A005070 A005071 A005072 * A005074 A005075 A005076

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 09 2017

Status

approved