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 A269459 #23 Jun 23 2023 03:47:19
%S A269459 15,16,45,60,69,75,112,116,236,296,319,452,576,586,843,1047,1184,1704,
%T A269459 1902,2852,2966,3068,3122,4708,4805,5684,6150,6712,7126,10920,10950,
%U A269459 13107,16700,18698,27828,29309,31142,31448,31764,43152,48584,51609,53822,62472,63008
%N A269459 Numbers that are equal to the sum of the number of divisors of their first k arithmetic derivatives, for some k.
%e A269459 The first eight arithmetic derivatives of 75 are 55, 16, 32, 80, 176, 368, 752, 1520 and d(55) + d(16) + d(32) + d(80) + d(176) + d(368) + d(752) + d(1520) = 4 + 5 + 6 + 10 + 10 + 10 + 10 + 20 = 75.
%p A269459 with(numtheory): P:=proc(q) local a,b,k,n,p; for n from 1 to q do a:=0; k:=1; b:=n;
%p A269459 while a<n do b:=b*add(op(2,p)/op(1,p),p=ifactors(b)[2]); if b>0 then a:=a+tau(b); else break; fi; od;
%p A269459 if n=a then print(n); fi; od; end: P(10^6);
%o A269459 (PARI) ad(n) = if (n<1, 0, my(f = factor(n)); n*sum(k=1, #f~, f[k,2]/f[k,1]));
%o A269459 isok(n) = {ss = 0; kn = n; while (ss < n, der = ad(kn); if (der == 0, break); ss += numdiv(der); kn = der); ss == n;} \\ _Michel Marcus_, Apr 08 2016
%Y A269459 Cf. A000005, A003415, A270389, A270713.
%K A269459 nonn
%O A269459 1,1
%A A269459 _Paolo P. Lava_, Apr 06 2016
%E A269459 a(35)-a(45) from _Amiram Eldar_, Jun 23 2023