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

0,2

Links

Table of n, a(n) for n=0..43.

Example

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.

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 *)

Prog

(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;

Crossrefs

Cf. A024675, A377381.

Sequence in context: A000516 A182044 A000854 * A232517 A329009 A110908

Adjacent sequences: A377379 A377380 A377381 * A377383 A377384 A377385

Keyword

nonn,new

Author

Marius A. Burtea, Dec 05 2024

Status

approved