A344103 a(n) is the smallest number k >= 1 with exactly n divisors d, for which sigma(k) is divisible by d*sigma(d).

1, 10, 6, 30, 132, 546, 270, 120, 840, 672, 1560, 3960, 4320, 6048, 9120, 16380, 26208, 12180, 36540, 37380, 10920, 55692, 34440, 68040, 112140, 51480, 63840, 103320, 30240, 219960, 273000, 209160, 332640, 191520, 1136520, 393120, 594720, 1389960, 1239840

Offset: 1

Author

Marius A. Burtea, May 10 2021

Keywords

• nonn

Examples

			sigma(1) = 1 = 1*sigma(1).
sigma(10) = 18 = 18*(1*sigma(1)) = 3*(2*sigma(2)).
sigma(6) = 12 = 12*(1*sigma(1)) = 2*(2*sigma(2)) = 1*(3*sigma(3)).
sigma(30) = 72 = 72*(1*sigma(1)) = 11*(2*sigma(2)) = 6*(3*sigma(3)) = 1*(6*sigma(6)) .
		

Crossrefs

Cf. A000203, A339472, A344102.

Programs

Magma

sd:=func; a:=[];  for n in [1..32] do k:=1; while #[d:d in Divisors(k)|sd(k,d)] ne n do k:=k+1; end while; Append(~a,k); end for; a;

Mathematica

a[n_] := Module[{k = 1}, While[Count[Divisors[k], ?(Divisible[DivisorSigma[1, k], # * DivisorSigma[1, #]] &)] != n, k++]; k]; Array[a, 25] (* _Amiram Eldar, May 12 2021 *)

PARI

isok(k, n) = my(sk=sigma(k)); sumdiv(k, d, (sk % (d*sigma(d))) == 0) == n;
a(n) = my(k=1); while (!isok(k, n), k++); k; \\ Michel Marcus, May 12 2021