A357034 a(n) is the smallest number with exactly n divisors that are hoax numbers (A019506).

1, 22, 308, 638, 3696, 4212, 18480, 26400, 55080, 52800, 73920, 108108, 220320, 216216, 275400, 324324, 432432, 550800, 734400, 1908000, 1144800, 1101600, 1377000, 1652400, 3027024, 2203200, 4039200, 2754000, 3304800, 5724000, 6528600, 9180000, 8586000, 5508000

Offset: 0

Author

Marius A. Burtea, Sep 20 2022

Keywords

• nonn
• base

Examples

			1 has no divisors in A019506, so a(0) = 1;
22 has divisors 1, 2, 11, 22, and 22 = A019506(1), so a(1) = 22.
308 has divisors 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308 and 22 = A019506(1), 308 = A019506(14), so a(2) = 308.
		

Crossrefs

Cf. A019506.

Programs

Magma

hoax:=func; a:=[]; for n in [0..33] do k:=1; while #[d:d in Set(Divisors(k)) diff {1}|hoax(d)] ne n do k:=k+1; end while; Append(~a,k); end for; a;

Mathematica

digitSum[n_] := Total @ IntegerDigits[n]; hoaxQ[n_] := CompositeQ[n] && Total[digitSum /@ FactorInteger[n][[;; , 1]]] == digitSum[n]; f[n_] := DivisorSum[n, 1 &, hoaxQ[#] &]; seq[len_, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < nmax, i = f[n] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[10, 10^5] (* Amiram Eldar, Sep 26 2022 *)