A005071 Sum of squares of primes = 1 mod 3 dividing n.

0, 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 169, 49, 0, 0, 0, 0, 361, 0, 49, 0, 0, 0, 0, 169, 0, 49, 0, 0, 961, 0, 0, 0, 49, 0, 1369, 361, 169, 0, 0, 49, 1849, 0, 0, 0, 0, 0, 49, 0, 0, 169, 0, 0, 0, 49, 361, 0, 0, 0, 3721, 961, 49, 0, 169, 0, 4489, 0, 0, 49, 0, 0, 5329, 1369, 0, 361, 49, 169, 6241, 0, 0, 0, 0, 49, 0, 1849, 0, 0, 0, 0, 218

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Cf. A000290, A005070, A005072, A005073.

Programs

Mathematica

Module[{sp=Select[Prime[Range[100]],Mod[#,3]==1&]},Table[Total[ Select[ sp, Divisible[ n,#]&]^2],{n,70}]] (* Harvey P. Dale, Dec 19 2014 *)
f[p_, e_] := If[Mod[p, 3] == 1, p^2, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

Scheme

(define (A005071 n) (if (= 1 n) 0 (+ (A000290 (if (= 1 (modulo (A020639 n) 3)) (A020639 n) 0)) (A005071 (A028234 n))))) ;; Antti Karttunen, Jul 09 2017

Formula

Additive with a(p^e) = p^2 if p = 1 (mod 3), 0 otherwise.

Extensions

More terms from Antti Karttunen, Jul 09 2017