%I #21 Sep 08 2022 08:46:08
%S 5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
%T 30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
%U 53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71
%N Numbers n such that A242962(n) = sigma(n) = A000203(n).
%C A242962(n) = (n*(n+1)/2) mod antisigma(n) = A000217(n) mod A024816(n).
%C Union of number 5 and numbers >= 7.
%C Conjecture: this sequence lists all the positive integers n such that, for some integer k, (sin(k*Pi/n))^2 is irrational. - _Lorenzo Sauras Altuzarra_, Jan 27 2020
%H Michael De Vlieger, <a href="/A242963/b242963.txt">Table of n, a(n) for n = 1..14995</a>
%t Select[Range[3, 71], DivisorSigma[1, #] == Mod[PolygonalNumber@ #, Total@ Complement[Range@ #, Divisors@ #]] &] (* _Michael De Vlieger_, Jan 28 2020 *)
%o (Magma) [n: n in [3..100000] | ((n*(n+1)div 2) mod (n*(n+1)div 2-SumOfDivisors(n))) eq (SumOfDivisors(n))]
%Y Cf. A000203, A000217, A002961, A024816, A242962, A243117, A243118, A217290, A009005.
%K nonn
%O 1,1
%A _Jaroslav Krizek_, May 29 2014