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%I #17 Nov 23 2023 11:25:22
%S 1,2,12,52,75,90,98,150,338,528,560,722,867,912,1452,1456,1525,1734,
%T 1922,2064,2340,2890,3050,3120,3216,3698,4144,4950,5043,6348,6516,
%U 6804,7350,7824,8176,8880,9024,9920,10086,10128,10304,10443,10658,11340,11858,13584
%N Numbers k such that k and the sum of the divisors of k have the same prime signature.
%C 2 is the only prime. - _Michel Marcus_, Mar 10 2018
%H Alois P. Heinz, <a href="/A300572/b300572.txt">Table of n, a(n) for n = 1..3000</a>
%F { k | A046523(k) = A046523(A000203(k)) }.
%p s:= n-> sort(map(i-> i[2], ifactors(n)[2])):
%p a:= proc(n) option remember; local k; for k from 1+
%p a(n-1) while s(k)<>s(numtheory[sigma](k)) do od; k
%p end: a(0):=0:
%p seq(a(n), n=1..60);
%t okQ[k_] := Sort@FactorInteger[k][[All, 2]] == Sort@FactorInteger[DivisorSigma[1, k]][[All, 2]];
%t Select[Range[10^5], okQ] (* _Jean-François Alcover_, Nov 23 2023 *)
%o (PARI) isok(k) = vecsort(factor(k)[, 2]) == vecsort(factor(sigma(k))[, 2]); \\ _Michel Marcus_, Mar 10 2018
%Y Cf. A000203, A008578, A046523, A300216, A300573.
%K nonn
%O 1,2
%A _Alois P. Heinz_, Mar 08 2018
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