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%I #26 Oct 24 2024 09:25:19
%S 1,2,1,3,1,2,1,1,3,1,2,1,1,1,2,1,1,2,1,1,1,2,1,1,1,1,1,1,1,3,2,1,1,1,
%T 1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,2,1,1,1,1,1,1,2,
%U 1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N Number of times n appears in A362965 (number of primes <= the n-th prime power).
%C Conjecture: a(n) can be only 1, 2, or 3 (with the first occurrences of 3 appearing at n = 4, 9, 30, 327 and 3512).
%H Paolo Xausa, <a href="/A366833/b366833.txt">Table of n, a(n) for n = 1..10000</a>
%H Paolo Xausa, <a href="/A366833/a366833.png">1200 X 1200 raster image of a(n)</a>, n = 1..1440000, read left to right, top to bottom, showing a(n) = 1 in blue, a(n) = 2 in white and a(n) = 3 in red.
%t With[{upto=1000},Map[Length,Most[Split[PrimePi[Select[Range[upto],PrimePowerQ]]]]]] (* Considers prime powers up to 1000 *)
%Y Run lengths of A362965.
%Y Cf. A068435, A075526, A246655, A366835.
%K nonn
%O 1,2
%A _Paolo Xausa_, Oct 25 2023