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%I #8 Apr 16 2023 02:17:43
%S 3,4,6,7,8,9,11,12,14,16,18,19,20,22,23,24,26,27,28,31,32,34,36,38,40,
%T 42,43,44,46,47,48,49,50,52,54,56,58,59,60,62,64,66,67,68,70,71,72,74,
%U 76,78,79,80,81,82,83,84,86,88,90,92,94,96,98,100,102,103
%N Hypertotient numbers: numbers k such that the set that includes k and the numbers less than k and relatively prime to k can be partitioned into two disjoint subsets of equal sum.
%C With the exception of 10 and 30, these are numbers k such that k*(phi(k)+2) is divisible by 4, where phi is the Euler totient function (A000010).
%H Amiram Eldar, <a href="/A362287/b362287.txt">Table of n, a(n) for n = 1..10000</a>
%H Shahbaz Ali and Khalid Mahmood, <a href="https://ijmex.com/index.php/ijmex/article/view/975">New numbers on Euler's totient function with applications</a>, Journal of Mathematical Extension, Vol. 14, No. 1 (2020), pp. 61-83.
%e 6 is a term since the set {1, 5, 6} can be partitioned into two disjoint subsets, {1, 5} and {6}, of equal sum.
%t Select[Range[120], ! MemberQ[{10, 30}, #] && Divisible[# * (EulerPhi[#] + 2), 4] &]
%o (PARI) is(n) = n != 10 && n != 30 && !((n * (eulerphi(n) + 2)) % 4);
%Y Cf. A000010, A332556.
%K nonn
%O 1,1
%A _Amiram Eldar_, Apr 14 2023
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