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 A333926 #10 Apr 11 2020 05:36:39 %S A333926 1,3,4,7,6,12,8,11,13,18,12,28,14,24,24,23,18,39,20,42,32,36,24,44,31, %T A333926 42,31,56,30,72,32,35,48,54,48,91,38,60,56,66,42,96,44,84,78,72,48,92, %U A333926 57,93,72,98,54,93,72,88,80,90,60,168,62,96,104,79,84,144 %N A333926 The sum of recursive divisors of n. %C A333926 The definition of recursive divisors and the number of recursive divisors of n are in A282446. %C A333926 First differs from A051378 at n = 256. %H A333926 Amiram Eldar, <a href="/A333926/b333926.txt">Table of n, a(n) for n = 1..10000</a> %F A333926 Multiplicative with a(p^k) = 1 + Sum_{d recursive divisor of k} p^d. %F A333926 a(n) <= A051378(n) <= A000203(n). %e A333926 The recursive divisors of 8 are 1, 2 and 8, therefore a(8) = 1 + 2 + 8 = 11. %t A333926 recDivQ[n_, 1] = True; recDivQ[n_, d_] := recDivQ[n, d] = Divisible[n, d] && AllTrue[FactorInteger[d], recDivQ[IntegerExponent[n, First[#]], Last[#]] &]; recDivs[n_] := Select[Divisors[n], recDivQ[n, #] &]; f[p_, e_] := 1 + Total[p^recDivs[e]]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] %Y A333926 Cf. A000203, A051378, A282446, A287957, A287958. %K A333926 nonn,mult %O A333926 1,2 %A A333926 _Amiram Eldar_, Apr 10 2020