|
%I #15 Sep 07 2018 04:01:20
%S 1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,4,4,4,4,5,5,6,6,7,8,9,9,10,10,12,
%T 12,13,14,16,16,18,19,21,23,26,27,29,30,34,35,39,43,48,51,55,57,63,67,
%U 74,78,84,89,99,103,112,119,132,139,148,156,170,182,199
%N Number of integer partitions of n whose sum of reciprocals squared is an integer.
%C From _David A. Corneth_, Sep 03 2018: (Start)
%C Let a valid tuple be a tuple of positive integers whose sum of reciprocals squared is an integer. Initially one only needs to consider tuples of positive integers where each element is > 1. After that some ones could be prepended to a valid tuple to find new valid tuples.
%C One could define a prime tuple as a valid tuple where no proper part with elements is a valid tuple. So (1) would be a prime tuple as no proper part of (1) has elements and is a valid tuple. Other examples of prime tuples are (2, 2, 2, 2) and (2, 2, 2, 3, 3, 6).
%C The list of distinct elements in a tuple could be whittled down by finding for each positive integer m the least sum of a prime tuple in which that integer is. For each m, that sum is at most m^3. (End)
%H Giovanni Resta, <a href="/A318585/b318585.txt">Table of n, a(n) for n = 1..130</a>
%e The a(26) = 7 integer partitions:
%e (6332222222)
%e (44442221111)
%e (63322211111111)
%e (22222222222211)
%e (222222221111111111)
%e (2222111111111111111111)
%e (11111111111111111111111111)
%t Table[Length[Select[IntegerPartitions[n],IntegerQ[Total[#^(-2)]]&]],{n,30}]
%Y Cf. A000041, A002865, A051908, A058360, A289506, A289507, A316854, A316856.
%Y Cf. A316854, A318584, A318586, A318587, A318588, A318589.
%K nonn
%O 1,8
%A _Gus Wiseman_, Aug 29 2018
%E a(61)-a(70) from _Giovanni Resta_, Sep 03 2018
|
