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%I #9 Aug 05 2023 22:02:48
%S 1,3,6,12,18,48,36,192,72,84,144,3072,168,5985,576,336,504,26505,672,
%T 45045,840,1344,6510,129675,2016,1680,11970,4620,4032,389025,3360,
%U 888615,6552,13020,53010,6720,8736,855855,90090,23940,13104,2411955,17472,2417415,26040
%N a(n) is the smallest number k with exactly n of its divisors in A052294.
%e a(0) = 1 because 1 has no divisors in A052294.
%e 2 has no divisors in A052294 and 3 has only one divisor 3 = 11_2 in A052294, so a(1) = 3.
%e 4 has no divisors in A052294, 5 has only the divisor 5 = 101_2 in A052294, 6 has divisors 3 = 11_2 and 6 = 110_2, so a(2) = 6.
%t seq[len_, kmax_] := Module[{s = Table[0, {len}], c = 0, k = 1, ind}, While[k < kmax && c < len, ind = DivisorSum[k, 1 &, PrimeQ[DigitCount[#, 2, 1]] &] + 1; If[ind <= len && s[[ind]] == 0, c++; s[[ind]] = k]; k++]; s]; seq[40, 10^6] (* _Amiram Eldar_, Jul 10 2023 *)
%o (Magma) fp:=func<n|IsPrime(Multiplicity(Intseq(n,2),1)) >; a:=[]; for n in [0..44] do k:= 1; while #[d:d in Divisors(k)|fp(d)] ne n do k:=k+1; end while; Append(~a,k); end for; a;
%o (PARI) a(n) = my(k=1); while (sumdiv(k, d, isprime(hammingweight(d))) != n, k++); k; \\ _Michel Marcus_, Jul 10 2023
%Y Cf. A052294.
%K nonn,base
%O 0,2
%A _Marius A. Burtea_, Jul 08 2023
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