A005083 Sum of squares of primes = 3 mod 4 dividing n.

0, 0, 9, 0, 0, 9, 49, 0, 9, 0, 121, 9, 0, 49, 9, 0, 0, 9, 361, 0, 58, 121, 529, 9, 0, 0, 9, 49, 0, 9, 961, 0, 130, 0, 49, 9, 0, 361, 9, 0, 0, 58, 1849, 121, 9, 529, 2209, 9, 49, 0, 9, 0, 0, 9, 121, 49, 370, 0, 3481, 9, 0, 961, 58, 0, 0, 130, 4489, 0, 538, 49, 5041, 9, 0, 0, 9, 361, 170, 9, 6241, 0, 9, 0, 6889, 58

Offset

1,3

Links

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

Formula

Additive with a(p^e) = p^2 if p = 3 (mod 4), 0 otherwise.

a(n) = A005063(n) - A005079(n) - 4*A059841(n). - Antti Karttunen, Jul 11 2017

Mathematica

Array[DivisorSum[#, #^2 &, And[PrimeQ@ #, Mod[#, 4] == 3] &] &, 84] (* Michael De Vlieger, Jul 11 2017 *)
f[p_, e_] := If[Mod[p, 4] == 3, p^2, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

Prog

(Scheme) (define (A005083 n) (if (= 1 n) 0 (+ (if (= 3 (modulo (A020639 n) 4)) (A000290 (A020639 n)) 0) (A005083 (A028234 n))))) ;; Antti Karttunen, Jul 11 2017
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (((p=f[k, 1])%4) == 3, p^2)); \\ Michel Marcus, Jul 11 2017

Crossrefs

Cf. A000290, A005063, A005079, A005082, A005084, A005085, A059841.

Sequence in context: A073052 A230068 A176908 * A050453 A338017 A341808

Adjacent sequences: A005080 A005081 A005082 * A005084 A005085 A005086

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 11 2017

Status

approved