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Number of strictly superior odd divisors of n.
29

%I #9 Feb 26 2021 06:32:38

%S 0,0,1,0,1,1,1,0,1,1,1,0,1,1,2,0,1,1,1,1,2,1,1,0,1,1,2,1,1,1,1,0,2,1,

%T 2,1,1,1,2,0,1,2,1,1,3,1,1,0,1,1,2,1,1,2,2,0,2,1,1,1,1,1,3,0,2,2,1,1,

%U 2,1,1,1,1,1,3,1,2,2,1,0,2,1,1,1,2,1,2,1,1,2,2,1,2,1,2,0,1,1,3,1,1,2,1,1,4

%N Number of strictly superior odd 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.

%H Antti Karttunen, <a href="/A341594/b341594.txt">Table of n, a(n) for n = 1..65537</a>

%e The a(n) divisors for n = 3, 15, 45, 105, 315, 405, 945, 1575, 1890:

%e 3 5 9 15 21 27 35 45 45

%e 15 15 21 35 45 45 63 63

%e 45 35 45 81 63 75 105

%e 105 63 135 105 105 135

%e 105 405 135 175 189

%e 315 189 225 315

%e 315 315 945

%e 945 525

%e 1575

%t Table[Length[Select[Divisors[n],OddQ[#]&&#>n/#&]],{n,100}]

%o (PARI) A341594(n) = sumdiv(n,d,(d%2)*(d>(n/d))); \\ _Antti Karttunen_, Feb 23 2021

%Y On odd indices, equals A056924 (number of strictly superior divisors).

%Y The inferior version is A069288.

%Y Positions of zeros are A116882.

%Y Positions of nonzero terms are A116883.

%Y The strictly inferior version is A333805.

%Y The version for squarefree instead of odd divisors is A341595.

%Y The version for prime instead of odd divisors is A341642.

%Y The version for prime-power instead of odd divisors is A341644.

%Y The superior version is A341675.

%Y A033676 selects the greatest inferior divisor.

%Y A033677 selects the smallest superior divisor.

%Y A038548 counts superior (or inferior) divisors.

%Y A140271 selects the smallest strictly superior divisor.

%Y A207375 lists central divisors.

%Y A341673 lists strictly superior divisors.

%Y - Inferior: A063962, A066839, A161906, A217581, A333749, A333750.

%Y - Superior: A051283, A059172, A063538, A063539, A070038, A161908, A341591, A341592, A341593, A341676.

%Y - Strictly Inferior: A060775, A070039, A333806, A341596, A341674.

%Y - Strictly Superior: A048098, A064052, A238535, A341643, A341645, A341646.

%Y Cf. A000005, A000203, A000265, A001222, A001248, A005408, A006530, A020639, A027193, A058695, A340101.

%K nonn

%O 1,15

%A _Gus Wiseman_, Feb 23 2021