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 A005064 #47 Jun 22 2024 19:03:10
%S A005064 0,8,27,8,125,35,343,8,27,133,1331,35,2197,351,152,8,4913,35,6859,133,
%T A005064 370,1339,12167,35,125,2205,27,351,24389,160,29791,8,1358,4921,468,35,
%U A005064 50653,6867,2224,133,68921,378,79507,1339,152,12175,103823,35,343,133,4940,2205,148877,35,1456,351,6886,24397,205379,160
%N A005064 Sum of cubes of primes dividing n.
%C A005064 The set of these terms is A213519. - _Bernard Schott_, Feb 11 2022
%C A005064 Inverse Möbius transform of n^3 * c(n), where c(n) is the prime characteristic (A010051). - _Wesley Ivan Hurt_, Jun 22 2024
%H A005064 Antti Karttunen, <a href="/A005064/b005064.txt">Table of n, a(n) for n = 1..10000</a>
%F A005064 Additive with a(p^e) = p^3.
%F A005064 G.f.: Sum_{k>=1} prime(k)^3*x^prime(k)/(1 - x^prime(k)). - _Ilya Gutkovskiy_, Dec 24 2016
%F A005064 From _Antti Karttunen_, Jul 11 2017: (Start)
%F A005064 a(n) = A005067(n) + 8*A059841(n).
%F A005064 a(n) = A005080(n) + A005084(n) + 8*A059841(n).
%F A005064 a(n) = A005072(n) + A005076(n) + 27*A079978(n).
%F A005064 (End)
%F A005064 Dirichlet g.f.: primezeta(s-3)*zeta(s). - _Benedict W. J. Irwin_, Jul 11 2018
%F A005064 a(n) = Sum_{p|n, p prime} p^3. - _Wesley Ivan Hurt_, Feb 04 2022
%F A005064 a(n) = Sum_{d|n} d^3 * c(d), where c = A010051. - _Wesley Ivan Hurt_, Jun 22 2024
%t A005064 Array[DivisorSum[#, #^3 &, PrimeQ] &, 60] (* _Michael De Vlieger_, Jul 11 2017 *)
%t A005064 f[p_, e_] := p^3; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jun 20 2022 *)
%o A005064 (Scheme) (define (A005064 n) (if (= 1 n) 0 (+ (A000578 (A020639 n)) (A005064 (A028234 n))))) ;; _Antti Karttunen_, Jul 10 2017
%o A005064 (Python)
%o A005064 from sympy import primefactors
%o A005064 def a(n): return sum(p**3 for p in primefactors(n))
%o A005064 print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Jul 11 2017
%o A005064 (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, f[k,1]^3); \\ _Michel Marcus_, Jul 11 2017
%Y A005064 Cf. A000578, A005067, A005072, A005076, A005080, A005084, A059841, A079978.
%Y A005064 Cf. A010051, A213519.
%Y A005064 Sum of the k-th powers of the primes dividing n for k=0..10 : A001221 (k=0), A008472 (k=1), A005063 (k=2), this sequence (k=3), A005065 (k=4), A351193 (k=5), A351194 (k=6), A351195 (k=7), this sequence (k=8), A351197 (k=9), A351198 (k=10).
%K A005064 nonn
%O A005064 1,2
%A A005064 _N. J. A. Sloane_
%E A005064 More terms from _Antti Karttunen_, Jul 10 2017