A005083 - OEIS

%I #20 Jun 21 2022 05:10:19

%S 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,

%T 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,

%U 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

%N Sum of squares of primes = 3 mod 4 dividing n.

%H Antti Karttunen, <a href="/A005083/b005083.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A005063(n) - A005079(n) - 4*A059841(n). - _Antti Karttunen_, Jul 11 2017

%t Array[DivisorSum[#, #^2 &, And[PrimeQ@ #, Mod[#, 4] == 3] &] &, 84] (* _Michael De Vlieger_, Jul 11 2017 *)

%t 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 *)

%o (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

%o (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

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

%K nonn

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _Antti Karttunen_, Jul 11 2017