A279064 - OEIS

%I #41 Oct 21 2018 18:58:22

%S 1,2,3,7,9,11,12,15,18,19,20,23,24,25,27,28,31,35,39,40,43,44,47,48,

%T 49,50,51,52,55,56,59,60,63,67,68,71,75,76,79,80,81,83,84,87,88,91,92,

%U 95,96,98,99,103,104,107,108,111,112,115,116,119,120,121,123,124,127,131

%N Numbers n such that the sum of numbers less than n that do not divide n is even.

%C Numbers n such that A000035(A024816(n)) = 0 or A000035(A000217(n)-A000203(n)) = 0.

%C There are 2 cases when n belongs to this sequence: 1) if n congruent to 0 or 3 mod 4 (A014601) and n is not square and is not twice square (A028983); 2) if n congruent to 1 or 2 mod 4 (A042963) and n is square or twice square (A028982).

%H Harvey P. Dale, <a href="/A279064/b279064.txt">Table of n, a(n) for n = 1..2000</a>

%e 12 is in the sequence because 12 has 6 divisors {1,2,3,4,6,12} therefore 6 non-divisors {5,7,8,9,10,11}, 5 + 7 + 8 + 9 + 10 + 11 = 50 and 50 is even.

%t Select[Range[150], Mod[#1 ((#1 + 1)/2) - DivisorSigma[1, #1], 2] == 0 & ]

%t Select[Range[150],EvenQ[(#(#+1))/2-DivisorSigma[1,#]]&] (* _Harvey P. Dale_, Oct 21 2018 *)

%o (PARI) isok(n) = (sum(k=1, n-1, k*((n % k) != 0)) % 2) == 0; \\ _Michel Marcus_, Dec 11 2016

%Y Cf. A000035, A000203, A000217, A014601, A024816, A028982, A028983, A042963, A053868, A053869, A274918.

%K nonn,easy

%O 1,2

%A _Ilya Gutkovskiy_, Dec 10 2016