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A005085 Sum of 4th powers of primes = 3 mod 4 dividing n.

%I A005085 #20 Jun 21 2022 05:10:23
%S A005085 0,0,81,0,0,81,2401,0,81,0,14641,81,0,2401,81,0,0,81,130321,0,2482,
%T A005085 14641,279841,81,0,0,81,2401,0,81,923521,0,14722,0,2401,81,0,130321,
%U A005085 81,0,0,2482,3418801,14641,81,279841,4879681,81,2401,0,81,0,0,81,14641,2401,130402,0,12117361,81,0,923521,2482,0,0,14722,20151121,0,279922
%N A005085 Sum of 4th powers of primes = 3 mod 4 dividing n.
%H A005085 Antti Karttunen, <a href="/A005085/b005085.txt">Table of n, a(n) for n = 1..10000</a>
%F A005085 Additive with a(p^e) = p^4 if p = 3 (mod 4), 0 otherwise.
%F A005085 a(n) = A005065(n) - A005081(n) - 16*A059841(n). - _Antti Karttunen_, Jul 11 2017
%t A005085 Array[DivisorSum[#, #^4 &, And[PrimeQ@ #, Mod[#, 4] == 3] &] &, 69] (* _Michael De Vlieger_, Jul 11 2017 *)
%t A005085 f[p_, e_] := If[Mod[p, 4] == 3, p^4, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jun 21 2022 *)
%o A005085 (Scheme) (define (A005085 n) (if (= 1 n) 0 (+ (if (= 3 (modulo (A020639 n) 4)) (A000583 (A020639 n)) 0) (A005085 (A028234 n))))) ;; _Antti Karttunen_, Jul 11 2017
%o A005085 (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (((p=f[k,1])%4) == 3, p^4)); \\ _Michel Marcus_, Jul 11 2017
%Y A005085 Cf. A000583, A005065, A005081, A005082, A005083, A005084, A059841.
%K A005085 nonn
%O A005085 1,3
%A A005085 _N. J. A. Sloane_
%E A005085 More terms from _Antti Karttunen_, Jul 11 2017