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 A005065 #36 Jun 22 2024 18:59:46
%S A005065 0,16,81,16,625,97,2401,16,81,641,14641,97,28561,2417,706,16,83521,97,
%T A005065 130321,641,2482,14657,279841,97,625,28577,81,2417,707281,722,923521,
%U A005065 16,14722,83537,3026,97,1874161,130337,28642,641,2825761,2498,3418801,14657,706,279857,4879681,97,2401,641,83602,28577,7890481,97
%N A005065 Sum of 4th powers of primes dividing n.
%C A005065 Primes are taken without multiplicity, e.g., 12 = 2*2*3, and a(12) = 2^4+3^4 = 97. - _Harvey P. Dale_, Jul 16 2014
%C A005065 Inverse Möbius transform of n^4 * c(n), where c(n) is the prime characteristic (A010051). - _Wesley Ivan Hurt_, Jun 22 2024
%H A005065 Antti Karttunen, <a href="/A005065/b005065.txt">Table of n, a(n) for n = 1..10000</a>
%F A005065 Additive with a(p^e) = p^4.
%F A005065 From _Antti Karttunen_, Jul 11 2017: (Start)
%F A005065 a(n) = A005068(n) + 16*A059841(n).
%F A005065 a(n) = A005081(n) + A005085(n) + 16*A059841(n).
%F A005065 a(n) = A005073(n) + A005077(n) + 81*A079978(n).
%F A005065 (End)
%F A005065 G.f.: Sum_{k>=1} prime(k)^4*x^prime(k)/(1 - x^prime(k)). - _Ilya Gutkovskiy_, Dec 24 2018
%F A005065 a(n) = Sum_{p|n, p prime} p^4. - _Wesley Ivan Hurt_, Feb 04 2022
%F A005065 a(n) = Sum_{d|n} d^4 * c(d), where c = A010051. - _Wesley Ivan Hurt_, Jun 22 2024
%p A005065 A005065 := proc(n)
%p A005065 add(d^4, d= numtheory[factorset](n)) ;
%p A005065 end proc;
%p A005065 seq(A005065(n),n=1..40) ; # _R. J. Mathar_, Nov 08 2011
%t A005065 Join[{0},Table[Total[Transpose[FactorInteger[n]][[1]]^4],{n,2,40}]] (* _Harvey P. Dale_, Jul 16 2014 *)
%t A005065 Array[DivisorSum[#, #^4 &, PrimeQ] &, 54] (* _Michael De Vlieger_, Jul 11 2017 *)
%o A005065 (Scheme) (define (A005065 n) (if (= 1 n) 0 (+ (A000583 (A020639 n)) (A005065 (A028234 n))))) ;; _Antti Karttunen_, Jul 10 2017
%o A005065 (Python)
%o A005065 from sympy import primefactors
%o A005065 def a(n): return sum(p**4 for p in primefactors(n))
%o A005065 print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Jul 11 2017
%o A005065 (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, f[k,1]^4); \\ _Michel Marcus_, Jul 11 2017
%Y A005065 Column k=4 of A322080.
%Y A005065 Cf. A000583, A005068, A005073, A005077, A005081, A005085, A008472, A059841, A079978.
%Y A005065 Sum of the k-th powers of the primes dividing n for k=0..10 : A001221 (k=0), A008472 (k=1), A005063 (k=2), A005064 (k=3), this sequence (k=4), A351193 (k=5), A351194 (k=6), A351195 (k=7), this sequence (k=8), A351197 (k=9), A351198 (k=10).
%Y A005065 Cf. A010051.
%K A005065 nonn
%O A005065 1,2
%A A005065 _N. J. A. Sloane_
%E A005065 More terms from _Antti Karttunen_, Jul 10 2017