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

0,2

Links

Table of n, a(n) for n=0..44.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A052294.

Sequence in context: A298029 A327328 A356019 * A074899 A345868 A318872

Adjacent sequences: A363460 A363461 A363462 * A363464 A363465 A363466

Keyword

nonn,base

Author

Marius A. Burtea, Jul 08 2023

Status

approved