A005082 - OEIS

%I #23 Jul 12 2017 05:26:38

%S 0,0,3,0,0,3,7,0,3,0,11,3,0,7,3,0,0,3,19,0,10,11,23,3,0,0,3,7,0,3,31,

%T 0,14,0,7,3,0,19,3,0,0,10,43,11,3,23,47,3,7,0,3,0,0,3,11,7,22,0,59,3,

%U 0,31,10,0,0,14,67,0,26,7,71,3,0,0,3,19,18,3,79,0,3,0,83,10,0,43,3,11,0,3,7,23,34,47,19,3,0,7,14,0,0,3,103

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

%H Antti Karttunen, <a href="/A005082/b005082.txt">Table of n, a(n) for n = 1..10000</a>

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

%F From _Antti Karttunen_, Jul 11 2017: (Start)

%F a(1) = 0; for n > 1, a(n) = (A079978(A020639(n) mod 4)*A020639(n)) + a(A028234(n)).

%F a(n) = A008472(n) - A005078(n) - 2*A059841(n).

%F (End)

%t Table[Total[Select[Transpose[FactorInteger[n]][[1]],Mod[#,4] == 3&]],{n,80}] (* _Harvey P. Dale_, Jan 18 2015 *)

%t Array[DivisorSum[#, # &, And[PrimeQ@ #, Mod[#, 4] == 3] &] &, 103] (* _Michael De Vlieger_, Jul 11 2017 *)

%o (Scheme) (define (A005082 n) (if (= 1 n) 0 (+ (* (A079978 (modulo (A020639 n) 4)) (A020639 n)) (A005082 (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)); \\ _Michel Marcus_, Jul 11 2017

%Y Cf. A005069, A005078, A005083, A005084, A005085, A008472, A059841.

%K nonn

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _Antti Karttunen_, Jul 11 2017