cp's OEIS Frontend

A341644 Number of strictly superior prime-power divisors of n.

%I A341644 #13 Nov 01 2024 05:16:31
%S A341644 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 A341644 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 A341644 1,0,1,1,1,1,1,1,1,1,1,1,2,1,1,0,1,1,1
%N A341644 Number of strictly superior prime-power divisors of n.
%C A341644 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.
%H A341644 Amiram Eldar, <a href="/A341644/b341644.txt">Table of n, a(n) for n = 1..10000</a>
%e A341644 The strictly superior prime power divisors of random selected n:
%e A341644 n = 768  2048  5103  6144  8192  8722  9433  9984
%e A341644    ----------------------------------------------
%e A341644      32    64    81   128   128        9433  128
%e A341644      64   128   243   256   256              256
%e A341644     128   256   729   512   512
%e A341644     256   512        1024  1024
%e A341644          1024        2048  2048
%e A341644          2048              4096
%e A341644                            8192
%t A341644 Table[Length[Select[Divisors[n],PrimePowerQ[#]&&#>n/#&]],{n,100}]
%o A341644 (PARI) a(n) = sumdiv(n, d, d^2 > n && isprimepower(d)); \\ _Amiram Eldar_, Nov 01 2024
%Y A341644 Positions of zeros (after the first) are A051283.
%Y A341644 The inferior version is A333750.
%Y A341644 Dominated by A341593 (the weakly superior version).
%Y A341644 The version for odd instead of prime divisors is A341594.
%Y A341644 The version for squarefree instead of prime divisors is A341595.
%Y A341644 The version for prime instead of prime-power divisors is A341642.
%Y A341644 The strictly inferior version is A341677.
%Y A341644 A000961 lists prime powers.
%Y A341644 A001221 counts prime divisors, with sum A001414.
%Y A341644 A001222 counts prime-power divisors.
%Y A341644 A005117 lists squarefree numbers.
%Y A341644 A140271 selects the smallest strictly superior divisor.
%Y A341644 A038548 counts superior (or inferior) divisors.
%Y A341644 A056924 counts strictly superior (or strictly inferior) divisors.
%Y A341644 A207375 list central divisors.
%Y A341644 A341673 lists strictly superior divisors.
%Y A341644 - Inferior: A033676, A063962, A066839, A069288, A161906, A217581, A333749.
%Y A341644 - Superior: A033677, A059172, A063538, A063539, A070038, A072500, A116882, A116883, A161908, A341591, A341592, A341675, A341676.
%Y A341644 - Strictly Inferior: A060775, A070039, A333805, A333806, A341596, A341674.
%Y A341644 - Strictly Superior: A048098, A064052, A238535, A341643, A341646.
%Y A341644 Cf. A000005, A000203, A001248, A006530, A020639, A112798.
%K A341644 nonn
%O A341644 1,8
%A A341644 _Gus Wiseman_, Feb 22 2021