cp's OEIS Frontend

A326644 Number of subsets of {1..n} containing n whose mean and geometric mean are both integers.

%I A326644 #9 Aug 03 2019 22:13:36
%S A326644 0,1,1,1,1,1,1,1,2,2,1,1,3,1,1,1,3,1,7,1,1,1,1,1,6,5,1,23,1,1,1,1,28,
%T A326644 1,1,1,38,1,1,1,5,1,1,1,1,6,1,1,81,8,28,1,1,1,126,1,6,1,1,1,37,1,1,6,
%U A326644 208,1,1,1,1,1,1,1,351,1,1,381,1,1,1,1,159,605,1,1,9,1,1,1,2,1,1223,1,1,1,1,1,805,1,113,2,5021,1,1,1,2,1,1,1,2630,1,1,1,54,1,1,1,1,2,1,1
%N A326644 Number of subsets of {1..n} containing n whose mean and geometric mean are both integers.
%H A326644 Wikipedia, <a href="https://en.wikipedia.org/wiki/Geometric_mean">Geometric mean</a>
%e A326644 The a(1) = 1 through a(12) = 3 subsets:
%e A326644   {1}  {2}  {3}  {4}  {5}  {6}  {7}  {8}    {9}    {10}  {11}  {12}
%e A326644                                      {2,8}  {1,9}              {3,6,12}
%e A326644                                                                {3,4,9,12}
%e A326644 The a(18) = 7 subsets:
%e A326644   {18}
%e A326644   {2,18}
%e A326644   {8,18}
%e A326644   {1,8,9,18}
%e A326644   {2,3,8,9,18}
%e A326644   {6,12,16,18}
%e A326644   {2,3,4,9,12,18}
%t A326644 Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]],{n,0,10}]
%Y A326644 First differences of A326643.
%Y A326644 Subsets whose mean is an integer are A051293.
%Y A326644 Subsets whose geometric mean is an integer are A326027.
%Y A326644 Partitions with integer mean and geometric mean are A326641.
%Y A326644 Strict partitions with integer mean and geometric mean are A326029.
%Y A326644 Cf. A067538, A067539, A082550, A082553, A102627, A326028, A326623, A326625, A326645, A326647.
%K A326644 nonn
%O A326644 0,9
%A A326644 _Gus Wiseman_, Jul 16 2019
%E A326644 More terms from _David Wasserman_, Aug 03 2019