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A274918 Numbers n such that the sum of numbers less than n that do not divide n is odd.

%I A274918 #38 Jul 29 2024 18:16:36
%S A274918 4,5,6,8,10,13,14,16,17,21,22,26,29,30,32,33,34,36,37,38,41,42,45,46,
%T A274918 53,54,57,58,61,62,64,65,66,69,70,72,73,74,77,78,82,85,86,89,90,93,94,
%U A274918 97,100,101,102,105,106,109,110,113,114,117,118,122,125,126,128,129,130,133,134,137,138,141,142,144,145,146,149,150
%N A274918 Numbers n such that the sum of numbers less than n that do not divide n is odd.
%C A274918 Numbers n such that A000035(A024816(n)) = 1 or A000035(A000217(n)-A000203(n)) = 1.
%C A274918 There are 2 cases when n belongs to this sequence: 1) if n congruent to 0 or 3 mod 4 (A014601) and n is square or twice square (A028982); 2) if n congruent to 1 or 2 mod 4 (A042963) and n is not square and is not twice square (A028983).
%H A274918 Robert Israel, <a href="/A274918/b274918.txt">Table of n, a(n) for n = 1..10000</a>
%e A274918 6 is in the sequence because 6 has 4 divisors {1,2,3,6} therefore 2 non-divisors {4,5}, 4 + 5 = 9 and 9 is odd.
%p A274918 filter:= n -> evalb(n+1 mod 4 <= 1) = (issqr(n) or issqr(n/2)):
%p A274918 select(filter, [$1..200]); # _Robert Israel_, Dec 11 2016
%t A274918 Select[Range[150], Mod[#1 ((#1 + 1)/2) - DivisorSigma[1, #1], 2] == 1 & ]
%t A274918 Select[Range[150],OddQ[Total[Complement[Range[#],Divisors[#]]]]&] (* _Harvey P. Dale_, Jul 29 2024 *)
%Y A274918 Cf. A000035, A000203, A000217, A014601, A024816, A028982, A028983, A042963, A053868, A053869, A279064.
%K A274918 nonn,easy
%O A274918 1,1
%A A274918 _Ilya Gutkovskiy_, Dec 10 2016