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%I #9 Jun 17 2022 22:13:08
%S 1,3,4,5,7,8,9,11,13,15,16,17,19,23,24,25,27,28,29,31,32,33,35,37,40,
%T 41,43,44,45,47,49,51,53,59,60,61,63,64,65,67,69,71,73,76,77,79,81,83,
%U 84,85,87,88,89,91,92,95,96,97,99,101,103,104,107,108,109,112,113,115,117,119,121,123,124,125,127,128,131
%N Numbers k such that A344005(d) < A344005(k) for all proper divisors d of k.
%t s[n_] := Module[{m = 1}, While[!Divisible[m*(m + 1), n], m++]; m]; q[n_] := Module[{sn = s[n]}, DivisorSum[n, If[s[#] < sn, 0, 1] &, # < n &] == 0]; Select[Range[150], q] (* _Amiram Eldar_, Jun 17 2022 *)
%o (PARI)
%o A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
%o A354993(n) = { my(x=A344005(n)); fordiv(n, d, if(A344005(d)==x, return(d==n))); };
%o isA354994(n) = A354993(n);
%Y Positions of 1's in A354991 and in A354999.
%Y Cf. A344005, A354993 (characteristic function).
%Y Cf. also A344881, A345944.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jun 17 2022
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