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%I #20 Nov 20 2021 11:33:15
%S 1,2,3,5,6,7,8,9,11,13,17,19,21,23,25,28,29,31,32,33,36,37,39,40,41,
%T 43,47,48,49,51,53,57,59,61,67,69,70,71,73,75,79,81,83,87,89,90,93,96,
%U 97,98,101,103,107,109,110,111,113,120,121,123,126,127,128,129,130
%N Numbers k such that A349410(k) = 1.
%C Does this sequence have density 1/3? This sequence has infinitely many terms because every prime number is a term.
%C The numbers of terms not exceeding 10^k for k = 1, 2, ... are 8, 50, 396, 3566, 33943, 332042, 3297317, 32983277, ... Apparently this sequence has an asymptotic density of about 0.33. - _Amiram Eldar_, Nov 18 2021
%t a[n_] := Module[{s = NestWhileList[n*DivisorSigma[0, #] &, 1, UnsameQ, All]}, Differences[Position[s, s[[-1]]]][[1, 1]]]; Select[Range[130], a[#] == 1 &] (* _Amiram Eldar_, Nov 18 2021 *)
%Y Cf. A349410.
%K nonn
%O 1,2
%A _Tejo Vrush_, Nov 18 2021
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