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%I #8 Feb 23 2021 08:29:36
%S 0,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,2,1,1,0,1,3,1,1,
%T 1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,0,1,1,1,3,1,1,1,1,
%U 1,0,1,1,1,1,1,1,1,1,1,1,2,1,1,0,1,1,1
%N Number of strictly superior prime-power divisors of n.
%C We define a divisor d|n to be strictly superior if d > n/d. Strictly superior divisors are counted by A056924 and listed by A341673.
%e The strictly superior prime power divisors of random selected n:
%e n = 768 2048 5103 6144 8192 8722 9433 9984
%e ----------------------------------------------
%e 32 64 81 128 128 9433 128
%e 64 128 243 256 256 256
%e 128 256 729 512 512
%e 256 512 1024 1024
%e 1024 2048 2048
%e 2048 4096
%e 8192
%t Table[Length[Select[Divisors[n],PrimePowerQ[#]&&#>n/#&]],{n,100}]
%Y Positions of zeros (after the first) are A051283.
%Y The inferior version is A333750.
%Y Dominated by A341593 (the weakly superior version).
%Y The version for odd instead of prime divisors is A341594.
%Y The version for squarefree instead of prime divisors is A341595.
%Y The version for prime instead of prime-power divisors is A341642.
%Y The strictly inferior version is A341677.
%Y A000961 lists prime powers.
%Y A001221 counts prime divisors, with sum A001414.
%Y A001222 counts prime-power divisors.
%Y A005117 lists squarefree numbers.
%Y A140271 selects the smallest strictly superior divisor.
%Y A038548 counts superior (or inferior) divisors.
%Y A056924 counts strictly superior (or strictly inferior) divisors.
%Y A207375 list central divisors.
%Y A341673 lists strictly superior divisors.
%Y - Inferior: A033676, A063962, A066839, A069288, A161906, A217581, A333749.
%Y - Superior: A033677, A059172, A063538, A063539, A070038, A072500, A116882, A116883, A161908, A341591, A341592, A341675, A341676.
%Y - Strictly Inferior: A060775, A070039, A333805, A333806, A341596, A341674.
%Y - Strictly Superior: A048098, A064052, A238535, A341643, A341646.
%Y Cf. A000005, A000203, A001248, A006530, A020639, A112798.
%K nonn
%O 1,8
%A _Gus Wiseman_, Feb 22 2021
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