A300573 Numbers k such that k and the sum of proper divisors of k have the same prime signature.

1, 6, 9, 14, 22, 28, 30, 33, 38, 46, 51, 62, 66, 84, 86, 87, 91, 92, 93, 102, 118, 132, 141, 142, 145, 158, 159, 166, 168, 170, 174, 182, 183, 188, 190, 206, 217, 219, 246, 247, 248, 249, 253, 262, 264, 267, 278, 280, 285, 295, 301, 308, 310, 316, 321, 326

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

{ k | A046523(k) = A046523(A001065(k)) }.

Maple

s:= n-> sort(map(i-> i[2], ifactors(n)[2])):
a:= proc(n) option remember; local k; for k from 1+
      a(n-1) while s(k)<>s(numtheory[sigma](k)-k) do od; k
    end: a(0):=0:
seq(a(n), n=1..80);

Mathematica

okQ[k_] := !PrimeQ[k] && Sort[FactorInteger[k][[All, 2]]] == Sort[FactorInteger[DivisorSigma[1, k] - k][[All, 2]]];
Select[Range[1000], okQ] (* Jean-François Alcover, Nov 23 2023 *)

Crossrefs

Cf. A001065, A008578, A046523, A300216, A300572.

Sequence in context: A316049 A316019 A316020 * A020717 A196993 A303162

Adjacent sequences: A300570 A300571 A300572 * A300574 A300575 A300576

Keyword

nonn

Author

Alois P. Heinz, Mar 08 2018

Status

approved