A357034 - OEIS

%I #12 Oct 14 2022 08:52:59

%S 1,22,308,638,3696,4212,18480,26400,55080,52800,73920,108108,220320,

%T 216216,275400,324324,432432,550800,734400,1908000,1144800,1101600,

%U 1377000,1652400,3027024,2203200,4039200,2754000,3304800,5724000,6528600,9180000,8586000,5508000

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

%e 1 has no divisors in A019506, so a(0) = 1;

%e 22 has divisors 1, 2, 11, 22, and 22 = A019506(1), so a(1) = 22.

%e 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.

%t 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 *)

%o (Magma) hoax:=func<n| not IsPrime(n) and (&+Intseq(n, 10) eq &+[ &+Intseq(p, 10): p in PrimeDivisors(n)])>; 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;

%Y Cf. A019506.

%K nonn,base

%O 0,2

%A _Marius A. Burtea_, Sep 20 2022