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 A384020 #14 May 28 2025 23:31:54
%S A384020 1,2,3,6,7,10,14,19,21,30,31,37,38,39,42,57,62,70,74,78,79,93,97,111,
%T A384020 114,133,139,157,158,186,190,194,199,210,211,217,222,229,237,259,266,
%U A384020 271,273,278,291,307,310,314,331,337,367,370,379,390,398,399,410
%N A384020 Numbers k > 0 such that sigma(A018804(k)) = k*tau(A018804(k)) where sigma denotes the sum of divisors (A000203) and tau denotes the number of divisors (A000005).
%C A384020 Experimental result: the fraction of numbers k such that S(P(k)) > k*D(P(k)) tends to 0, S(P(k)) = k*D(P(k)) tends to 0, S(P(k)) < k*D(P(k)) tends to 1 with growing k where S(P(k)) denotes A000203(A018804(k)) and D(P(k)) denotes A000005(A018804(k)).
%e A384020 For k = 6, a(6) = A000203(A018804(6)) = 6*A000005(A018804(6)).
%t A384020 f[p_, e_] := (e*(p - 1)/p + 1)*p^e; pil[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[500], Divide @@ DivisorSigma[{1, 0}, pil[#]] == # &] (* _Amiram Eldar_, May 17 2025 *)
%Y A384020 Cf. A000005, A000203, A018804, A382872.
%K A384020 nonn
%O A384020 1,2
%A A384020 _Ctibor O. Zizka_, May 17 2025