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

0,2

Links

Table of n, a(n) for n=0..33.

Example

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.

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 *)

Prog

(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;

Crossrefs

Cf. A019506.

Sequence in context: A028109 A003468 A120051 * A041928 A028054 A100789

Adjacent sequences: A357031 A357032 A357033 * A357035 A357036 A357037

Keyword

nonn,base

Author

Marius A. Burtea, Sep 20 2022

Status

approved