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%I #13 Jul 29 2023 15:59:14
%S 1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,19,20,21,22,23,24,25,26,27,28,
%T 29,30,31,32,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,
%U 56,57,58,59,60,61,62,63,64,71,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95
%N Numbers k for which A005940(k) >= k.
%C Sequence A005941(A364560(.)) sorted into ascending order.
%C A029747 is included as a subsequence, because it gives the known fixed points of map n -> A005940(n).
%C Differs from A343107 for the first time at a(22) = 25, which term is not present in A343107. On the other hand, 35 is the first term of A343107 that is not present in this sequence.
%t nn = 95; Array[Set[a[#], #] &, 2]; Do[If[EvenQ[n], Set[a[n], 2 a[n/2]], Set[a[n], Times @@ Power @@@ Map[{Prime[PrimePi[#1] + 1], #2} & @@ # &, FactorInteger[a[(n + 1)/2]]]]], {n, 3, nn}]; Select[Range[nn], a[#] >= # &] (* _Michael De Vlieger_, Jul 28 2023 *)
%o (PARI)
%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o isA364542(n) = (A005940(n)>=n);
%Y Positions of nonnegative terms in A364499.
%Y Complement of A364540.
%Y Cf. A005940, A005941, A029747 (subsequence), A343107 (not a subsequence), A364560.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 28 2023
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