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

1,7

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A000290, A005070, A005072, A005073.

Sequence in context: A272096 A115480 A214953 * A174696 A203506 A254617

Adjacent sequences: A005068 A005069 A005070 * A005072 A005073 A005074

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 09 2017

Status

approved