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A300573
Numbers k such that k and the sum of proper divisors of k have the same prime signature.
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 08 2018
STATUS
approved