A300572 Numbers k such that k and the sum of the divisors of k have the same prime signature.

1, 2, 12, 52, 75, 90, 98, 150, 338, 528, 560, 722, 867, 912, 1452, 1456, 1525, 1734, 1922, 2064, 2340, 2890, 3050, 3120, 3216, 3698, 4144, 4950, 5043, 6348, 6516, 6804, 7350, 7824, 8176, 8880, 9024, 9920, 10086, 10128, 10304, 10443, 10658, 11340, 11858, 13584

Offset

1,2

Comments

2 is the only prime. - Michel Marcus, Mar 10 2018

Links

Alois P. Heinz, Table of n, a(n) for n = 1..3000

Formula

{ k | A046523(k) = A046523(A000203(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)) do od; k
    end: a(0):=0:
seq(a(n), n=1..60);

Mathematica

okQ[k_] := Sort@FactorInteger[k][[All, 2]] == Sort@FactorInteger[DivisorSigma[1, k]][[All, 2]];
Select[Range[10^5], okQ] (* Jean-François Alcover, Nov 23 2023 *)

Prog

(PARI) isok(k) = vecsort(factor(k)[, 2]) == vecsort(factor(sigma(k))[, 2]); \\ Michel Marcus, Mar 10 2018

Crossrefs

Cf. A000203, A008578, A046523, A300216, A300573.

Sequence in context: A057547 A216648 A043007 * A176580 A179259 A261474

Adjacent sequences: A300569 A300570 A300571 * A300573 A300574 A300575

Keyword

nonn

Author

Alois P. Heinz, Mar 08 2018

Status

approved