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Sum of 4th powers of primes = 1 mod 4 dividing n.
6

%I #19 Jun 21 2022 05:10:14

%S 0,0,0,0,625,0,0,0,0,625,0,0,28561,0,625,0,83521,0,0,625,0,0,0,0,625,

%T 28561,0,0,707281,625,0,0,0,83521,625,0,1874161,0,28561,625,2825761,0,

%U 0,0,625,0,0,0,0,625,83521,28561,7890481,0,625,0,0,707281,0,625,13845841,0,0,0,29186,0,0,83521,0,625,0,0,28398241

%N Sum of 4th powers of primes = 1 mod 4 dividing n.

%H Antti Karttunen, <a href="/A005081/b005081.txt">Table of n, a(n) for n = 1..10000</a>

%F Additive with a(p^e) = p^4 if p = 1 (mod 4), 0 otherwise.

%F a(n) = A005065(n) - A005085(n) - 16*A059841(n). - _Antti Karttunen_, Jul 11 2017

%t Array[DivisorSum[#, #^4 &, And[PrimeQ@ #, Mod[#, 4] == 1] &] &, 73] (* _Michael De Vlieger_, Jul 11 2017 *)

%t f[p_, e_] := If[Mod[p, 4] == 1, p^4, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jun 21 2022 *)

%o (Scheme) (define (A005081 n) (if (= 1 n) 0 (+ (if (= 1 (modulo (A020639 n) 4)) (A000583 (A020639 n)) 0) (A005081 (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) == 1, p^4)); \\ _Michel Marcus_, Jul 11 2017

%Y Cf. A000583, A005065, A005078, A005079, A005080, A005085, A059841.

%K nonn

%O 1,5

%A _N. J. A. Sloane_

%E More terms from _Antti Karttunen_, Jul 11 2017