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 A387653 #6 Sep 05 2025 04:44:33
%S A387653 134504,636615,648584,1521975,1836135,2105144,2276504,2607255
%N A387653 Numbers k such that k and k+1 are both almost practical numbers (A174533).
%t A387653 almostPracQ[n_] := almostPracQ[n] = Module[{d = Divisors[n], c, x}, c = CoefficientList[Product[1 + x^i, {i, d}], x]; Count[Rest[c], _?(# > 0 &)] == Total[d] - 2];
%t A387653 Select[Range[135000], almostPracQ[#] && almostPracQ[#+1] &] (* warning: a slow program *)
%o A387653 (PARI) isA174533(k) = {my(d = divisors(k), nd = #d, s = vecsum(d), p = prod(i = 1, nd, 1 + 'x^d[i])); #select(x -> x > 0, Col(p)) + 1 == s;} \\ A174533
%o A387653 list(kmax) = {my(is1 = 0, is2); for(k = 2, kmax, is2 = isA174533(k); if(is1 && is2, print1(k-1, ", ")); is1 = is2);} \\ warning: a slow program
%Y A387653 Cf. A174533, A287681.
%Y A387653 Subsequence of A387654.
%K A387653 nonn,more,new
%O A387653 1,1
%A A387653 _Amiram Eldar_, Sep 05 2025