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%I #21 Jun 21 2022 05:10:40
%S 0,16,0,16,625,16,0,16,0,641,14641,16,0,16,625,16,83521,16,0,641,0,
%T 14657,279841,16,625,16,0,16,707281,641,0,16,14641,83537,625,16,0,16,
%U 0,641,2825761,16,0,14657,625,279857,4879681,16,0,641,83521,16,7890481,16,15266,16,0,707297,12117361,641,0,16,0,16,625,14657,0,83537
%N Sum of 4th powers of primes = 2 mod 3 dividing n.
%H Antti Karttunen, <a href="/A005077/b005077.txt">Table of n, a(n) for n = 1..10000</a>
%F Additive with a(p^e) = p^4 if p = 2 (mod 3), 0 otherwise.
%F a(n) = A005065(n) - A005073(n) - 81*A079978(n). - _Antti Karttunen_, Jul 10 2017
%t Array[DivisorSum[#, #^4 &, And[PrimeQ@ #, Mod[#, 3] == 2] &] &, 68] (* _Michael De Vlieger_, Jul 11 2017 *)
%t f[p_, e_] := If[Mod[p, 3] == 2, p^4, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jun 21 2022 *)
%o (Scheme) (define (A005077 n) (if (= 1 n) 0 (+ (A000583 (if (= 2 (modulo (A020639 n) 3)) (A020639 n) 0)) (A005077 (A028234 n))))) ;; _Antti Karttunen_, Jul 10 2017
%o (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (((p=f[k,1])%3) == 2, p^4)); \\ _Michel Marcus_, Jul 11 2017
%Y Cf. A000583, A005065, A005073, A005074, A005075, A005076, A008472, A079978.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Antti Karttunen_, Jul 10 2017
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