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A005080 Sum of cubes of primes = 1 mod 4 dividing n.

%I A005080 #21 Jun 21 2022 05:10:09
%S A005080 0,0,0,0,125,0,0,0,0,125,0,0,2197,0,125,0,4913,0,0,125,0,0,0,0,125,
%T A005080 2197,0,0,24389,125,0,0,0,4913,125,0,50653,0,2197,125,68921,0,0,0,125,
%U A005080 0,0,0,0,125,4913,2197,148877,0,125,0,0,24389,0,125,226981,0,0,0,2322,0,0,4913,0,125,0,0,389017,50653,125
%N A005080 Sum of cubes of primes = 1 mod 4 dividing n.
%H A005080 Antti Karttunen, <a href="/A005080/b005080.txt">Table of n, a(n) for n = 1..10000</a>
%F A005080 Additive with a(p^e) = p^3 if p = 1 (mod 4), 0 otherwise.
%F A005080 a(n) = A005064(n) - A005084(n) - 8*A059841(n). - _Antti Karttunen_, Jul 11 2017
%t A005080 Array[DivisorSum[#, #^3 &, And[PrimeQ@ #, Mod[#, 4] == 1] &] &, 75] (* _Michael De Vlieger_, Jul 11 2017 *)
%t A005080 f[p_, e_] := If[Mod[p, 4] == 1, p^3, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jun 21 2022 *)
%o A005080 (Scheme) (define (A005080 n) (if (= 1 n) 0 (+ (if (= 1 (modulo (A020639 n) 4)) (A000578 (A020639 n)) 0) (A005080 (A028234 n))))) ;; _Antti Karttunen_, Jul 11 2017
%o A005080 (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (((p=f[k,1])%4) == 1, p^3)); \\ _Michel Marcus_, Jul 11 2017
%Y A005080 Cf. A000578, A005064, A005078, A005079, A005081, A005084, A059841.
%K A005080 nonn
%O A005080 1,5
%A A005080 _N. J. A. Sloane_
%E A005080 More terms from _Antti Karttunen_, Jul 11 2017