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 A280385 #14 May 12 2021 02:06:53
%S A280385 0,4,13,17,42,55,104,108,117,146,267,280,449,502,536,540,829,842,1203,
%T A280385 1232,1290,1415,1944,1957,1982,2155,2164,2217,3058,3096,4057,4061,
%U A280385 4191,4484,4558,4571,5940,6305,6483,6512,8193,8255,10104,10229,10263,10796,13005,13018,13067,13096,13394,13567,16376,16389,16535
%N A280385 a(n) = Sum_{k=1..n} prime(k)^2*floor(n/prime(k)) .
%C A280385 Sum of all squares of prime divisors of all positive integers <= n.
%C A280385 Partial sums of A005063.
%H A280385 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F A280385 G.f.: (1/(1 - x))*Sum_{k>=1} prime(k)^2*x^prime(k)/(1 - x^prime(k)).
%e A280385 For n = 6 the prime divisors of the first six positive integers are {0}, {2}, {3}, {2}, {5}, {2, 3} so a(6) = 0^2 + 2^2 + 3^2 + 2^2 + 5^2 + 2^2 + 3^2 = 55.
%t A280385 Table[Sum[Prime[k]^2 Floor[n/Prime[k]], {k, 1, n}], {n, 55}]
%t A280385 Table[Sum[DivisorSum[k, #1^2 &, PrimeQ[#1] &], {k, 1, n}], {n, 55}]
%t A280385 nmax = 55; Rest[CoefficientList[Series[(1/(1 - x)) Sum[Prime[k]^2 x^Prime[k]/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x]]
%o A280385 (PARI) a(n) = sum(k=1, n, prime(k)^2 * (n\prime(k))); \\ _Indranil Ghosh_, Apr 03 2017
%o A280385 (Python)
%o A280385 from sympy import prime
%o A280385 print([sum([prime(k)**2 * (n//prime(k)) for k in range(1, n + 1)]) for n in range(1, 21)]) # _Indranil Ghosh_, Apr 03 2017
%Y A280385 Cf. A001157, A005063, A008472, A024924, A064602, A279847, A279910.
%K A280385 nonn,easy
%O A280385 1,2
%A A280385 _Ilya Gutkovskiy_, Jan 01 2017