cp's OEIS Frontend

A341645 Numbers without a strictly superior squarefree divisor.

%I A341645 #18 Feb 11 2024 08:52:22
%S A341645 1,4,8,9,16,25,27,32,36,48,49,54,64,72,81,96,100,108,121,125,128,144,
%T A341645 160,162,169,192,196,200,216,224,225,243,250,256,288,289,320,324,343,
%U A341645 361,375,384,392,400,405,432,441,448,484,486,500,512,529,567,576,625
%N A341645 Numbers without a strictly superior squarefree divisor.
%C A341645 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 A341645 Michael De Vlieger, <a href="/A341645/b341645.txt">Table of n, a(n) for n = 1..10000</a>
%e A341645 72 has strictly superior divisors {9,12,18,24,36,72} and squarefree divisors {1,2,3,6}, but the intersection is empty, so 72 is in the sequence.
%t A341645 Select[Range[100],Function[n,Select[Divisors[n],SquareFreeQ[#]&&#>n/#&]=={}]]
%o A341645 (PARI) isok(m) = my(d=divisors(m)); #select(x->(issquarefree(x) && (x^2>m)), d) == 0; \\ _Michel Marcus_, Feb 11 2024
%Y A341645 The version for prime instead of squarefree divisors is A048098.
%Y A341645 The version for prime-power instead of squarefree divisors is A051283.
%Y A341645 The weakly superior version is A059172.
%Y A341645 The version for odd instead of squarefree divisors is A116882.
%Y A341645 Positions of zeros in A341595.
%Y A341645 The complement is A341646.
%Y A341645 A001221 counts prime divisors, with sum A001414.
%Y A341645 A005117 lists squarefree numbers.
%Y A341645 A038548 counts superior (or inferior) divisors.
%Y A341645 A056924 counts strictly superior (or strictly inferior) divisors.
%Y A341645 A140271 selects the smallest strictly superior divisor.
%Y A341645 A207375 list central divisors.
%Y A341645 A341673 lists strictly superior divisors.
%Y A341645 - Inferior: A033676, A063962, A066839, A069288, A161906, A217581, A333749.
%Y A341645 - Superior: A033677, A063538, A063539, A070038, A072500, A116883, A161908, A341591, A341592, A341593, A341675, A341676.
%Y A341645 - Strictly Inferior: A060775, A070039, A333805, A333806, A341596, A341674.
%Y A341645 - Strictly Superior: A064052, A238535, A341594, A341642, A341643, A341644.
%Y A341645 Cf. A000005, A000203, A001222, A001248, A006530, A020639, A112798.
%K A341645 nonn
%O A341645 1,2
%A A341645 _Gus Wiseman_, Feb 22 2021