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 A377382 #8 Dec 21 2024 01:03:30
%S A377382 1,4,52,12,162,36,60,120,240,300,180,600,360,1560,720,1260,1440,1620,
%T A377382 2520,2880,3240,5040,10920,6300,9360,10080,12960,12600,15840,20160,
%U A377382 22680,25200,31680,39600,27720,59400,50400,70560,56700,79200,55440,65520,83160,100800
%N A377382 a(n) is the smallest number k for which exactly n of its divisors are interprime numbers (A024675).
%e A377382 Because A024675(1) = 4 it follows that a(0) = 1 and a(1) = 4.
%e A377382 a(2) = 52 because 52 has the divisors 4 = A024675(1), 26 = A024675(8) and no number from 1 to 51 has exactly two interprime divisors.
%t A377382 d[n_] := DivisorSum[n, 1 &, CompositeQ[#] && NextPrime[#] + NextPrime[#, -1] == 2*# &]; seq[len_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len, i = d[n] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[44] (* _Amiram Eldar_, Dec 11 2024 *)
%o A377382 (Magma) ipr:=func<n|n ge 3 and not IsPrime(n) and 2*n eq NextPrime(n)+PreviousPrime(n)>; a:=[]; for n in [0..43] do k:=1; while #[d:d in Divisors(k)|ipr(d)] ne n do k:=k+1; end while; Append(~a,k); end for; a;
%Y A377382 Cf. A024675, A377381.
%K A377382 nonn
%O A377382 0,2
%A A377382 _Marius A. Burtea_, Dec 05 2024