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 A240112 #33 Feb 13 2025 08:27:09
%S A240112 4,9,12,16,18,20,25,28,36,44,45,48,49,50,52,60,63,64,68,75,76,80,81,
%T A240112 84,90,92,98,99,100,108,112,116,117,121,124,126,132,140,144,147,148,
%U A240112 150,153,156,162,164,169,171,172,175,176,180,188,192,196,198,204,207
%N A240112 Numbers for which the values of the Dedekind psi function (A001615) are greater than the values of the infinitary Dedekind psi function (A049417).
%C A240112 The first term of A072587 that is not in this sequence is 72.
%C A240112 On the set of the nonsquarefree numbers (A013929) it is complement to A240111.
%C A240112 The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 2, 29, 284, 2845, 28527, 285352, 2853422, 28534455, 285344362, 2853443344, ... . Apparently, the asymptotic density of this sequence exists and equals 0.2853443... . - _Amiram Eldar_, Feb 13 2025
%H A240112 Amiram Eldar, <a href="/A240112/b240112.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Peter J. C. Moses)
%t A240112 f1[p_, e_] := Module[{b = IntegerDigits[e, 2]}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; f2[p_, e_] := (p+1)*p^(e-1); q[1] = False; q[n_] := Module[{fct = FactorInteger[n]}, Times @@ f2 @@@ fct > Times @@ f1 @@@ fct]; Select[Range[250], q] (* _Amiram Eldar_, Feb 13 2025 *)
%o A240112 (PARI) isok(k) = {my(f = factor(k), b); prod(i=1, #f~, (f[i, 1]+1)*f[i, 1]^(f[i, 2]-1)) > prod(i=1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], 1+f[i, 1]^(2^(#b-k)), 1)));} \\ _Amiram Eldar_, Feb 13 2025
%Y A240112 Cf. A001615, A013929, A049417, A072587, A240111.
%K A240112 nonn
%O A240112 1,1
%A A240112 _Vladimir Shevelev_, Apr 01 2014
%E A240112 More terms from _Peter J. C. Moses_, Apr 02 2014