Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Dec 21 2024 01:03:30
%S 1,4,52,12,162,36,60,120,240,300,180,600,360,1560,720,1260,1440,1620,
%T 2520,2880,3240,5040,10920,6300,9360,10080,12960,12600,15840,20160,
%U 22680,25200,31680,39600,27720,59400,50400,70560,56700,79200,55440,65520,83160,100800
%N a(n) is the smallest number k for which exactly n of its divisors are interprime numbers (A024675).
%e Because A024675(1) = 4 it follows that a(0) = 1 and a(1) = 4.
%e 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 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 (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 Cf. A024675, A377381.
%K nonn
%O 0,2
%A _Marius A. Burtea_, Dec 05 2024