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 A347157 #5 Aug 20 2021 22:52:24 %S A347157 0,0,0,0,0,8,0,8,0,8,0,35,0,8,27,8,0,35,0,8,27,8,0,35,0,8,27,8,0,160, %T A347157 0,8,27,8,125,35,0,8,27,133,0,35,0,8,152,8,0,35,0,133,27,8,0,35,125, %U A347157 351,27,8,0,160,0,8,370,8,125,35,0,8,27,476,0,35,0,8,152 %N A347157 Sum of cubes of distinct prime divisors of n that are < sqrt(n). %F A347157 G.f.: Sum_{k>=1} prime(k)^3 * x^(prime(k)*(prime(k) + 1)) / (1 - x^prime(k)). %t A347157 Table[DivisorSum[n, #^3 &, # < Sqrt[n] && PrimeQ[#] &], {n, 1, 75}] %t A347157 nmax = 75; CoefficientList[Series[Sum[Prime[k]^3 x^(Prime[k] (Prime[k] + 1))/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest %Y A347157 Cf. A001158, A005064, A005067, A333806, A333808, A339354, A347156, A347158. %K A347157 nonn %O A347157 1,6 %A A347157 _Ilya Gutkovskiy_, Aug 20 2021