A339472 -id:A339472 - cp's OEIS frontend

A344102 Numbers k with at least two divisors d for which sigma(k) = d*sigma(d).

16380, 290160, 475020, 1372140, 4754880, 5284356, 5624892, 7033572, 8414640, 10322676, 12203100, 12724908, 16435692, 16655184, 24306480, 35675640, 36203076, 39792060, 43266132, 49758720, 55040076, 68229252, 70142436, 74662476, 76527360, 77084280, 82833660

Offset: 1

Marius A. Burtea, May 10 2021

nonn

			sigma(16380) = 156*sigma(156) = 182*sigma(182).
sigma(16655184) = 4368*sigma(4368) = 4836*sigma(4836) = 5642*sigma(5642).

Cf. A000203, A339472, A344103.

s:=func;  [n: n in [1..1000000]|#s(n) ge 2];

Select[Range[1.5*10^6], Count[(d = Divisors[#]) * DivisorSigma[1, d], DivisorSigma[1, #]] > 1 &] (* Amiram Eldar, May 12 2021 *)

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

Original entry on oeis.org

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

Marius A. Burtea, May 10 2021

nonn

			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)) .

Cf. A000203, A339472, A344102.

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;

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 *)

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

cp's OEIS Frontend

A344102 Numbers k with at least two divisors d for which sigma(k) = d*sigma(d).

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