A377382 a(n) is the smallest number k for which exactly n of its divisors are interprime numbers (A024675).

1, 4, 52, 12, 162, 36, 60, 120, 240, 300, 180, 600, 360, 1560, 720, 1260, 1440, 1620, 2520, 2880, 3240, 5040, 10920, 6300, 9360, 10080, 12960, 12600, 15840, 20160, 22680, 25200, 31680, 39600, 27720, 59400, 50400, 70560, 56700, 79200, 55440, 65520, 83160, 100800

Offset: 0

Author

Marius A. Burtea, Dec 05 2024

Keywords

• nonn

Examples

			Because A024675(1) = 4 it follows that a(0) = 1 and a(1) = 4.
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.
		

Crossrefs

Cf. A024675, A377381.

Programs

Magma

ipr:=func; 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;

Mathematica

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 *)