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%I #24 Nov 25 2024 12:15:24
%S 1,2,6,24,28,120,496,672,4320,4680,8128,26208,30240,32760,523776,
%T 2178540,8910720,17428320,20427264,23569920,33550336,45532800,
%U 91963648,142990848,197064960,459818240,1379454720,1476304896,8583644160,8589869056,10200236032
%N Numbers k that divide 2*sigma(k).
%C Numbers k such that 2*A000203(k) / k is an integer.
%C Union of A007691 (multiply-perfect numbers) and A159907 (numbers with half-integral abundancy index).
%H Jens Kruse Andersen, <a href="/A246454/b246454.txt">Table of n, a(n) for n = 1..55</a>
%e Number 24 is in the sequence because 24 divides 2*sigma(24); 24 divides 2*60.
%o (Magma) [n: n in [1..1000000] | Denominator(2*(SumOfDivisors(n))/n) eq 1];
%o (PARI)
%o for(n=1,10^8,if((2*sigma(n))%n==0,print1(n,", "))) \\ _Derek Orr_, Aug 26 2014
%Y Cf. A000203, A007691, A159907.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Aug 26 2014