A363463 a(n) is the smallest number k with exactly n of its divisors in A052294.

1, 3, 6, 12, 18, 48, 36, 192, 72, 84, 144, 3072, 168, 5985, 576, 336, 504, 26505, 672, 45045, 840, 1344, 6510, 129675, 2016, 1680, 11970, 4620, 4032, 389025, 3360, 888615, 6552, 13020, 53010, 6720, 8736, 855855, 90090, 23940, 13104, 2411955, 17472, 2417415, 26040

Offset: 0

Author

Marius A. Burtea, Jul 08 2023

Keywords

• nonn
• base

Examples

			a(0) = 1 because 1 has no divisors in A052294.
2 has no divisors in A052294 and 3 has only one divisor 3 = 11_2 in A052294, so a(1) = 3.
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.
		

Crossrefs

Cf. A052294.

Programs

Magma

fp:=func; 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;

Mathematica

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 *)

PARI

a(n) = my(k=1); while (sumdiv(k, d, isprime(hammingweight(d))) != n, k++); k; \\ Michel Marcus, Jul 10 2023