This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A005081 #19 Jun 21 2022 05:10:14 %S A005081 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 A005081 28561,0,0,707281,625,0,0,0,83521,625,0,1874161,0,28561,625,2825761,0, %U A005081 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 A005081 Sum of 4th powers of primes = 1 mod 4 dividing n. %H A005081 Antti Karttunen, <a href="/A005081/b005081.txt">Table of n, a(n) for n = 1..10000</a> %F A005081 Additive with a(p^e) = p^4 if p = 1 (mod 4), 0 otherwise. %F A005081 a(n) = A005065(n) - A005085(n) - 16*A059841(n). - _Antti Karttunen_, Jul 11 2017 %t A005081 Array[DivisorSum[#, #^4 &, And[PrimeQ@ #, Mod[#, 4] == 1] &] &, 73] (* _Michael De Vlieger_, Jul 11 2017 *) %t A005081 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 A005081 (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 A005081 (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 A005081 Cf. A000583, A005065, A005078, A005079, A005080, A005085, A059841. %K A005081 nonn %O A005081 1,5 %A A005081 _N. J. A. Sloane_ %E A005081 More terms from _Antti Karttunen_, Jul 11 2017