

A279064


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


2



1, 2, 3, 7, 9, 11, 12, 15, 18, 19, 20, 23, 24, 25, 27, 28, 31, 35, 39, 40, 43, 44, 47, 48, 49, 50, 51, 52, 55, 56, 59, 60, 63, 67, 68, 71, 75, 76, 79, 80, 81, 83, 84, 87, 88, 91, 92, 95, 96, 98, 99, 103, 104, 107, 108, 111, 112, 115, 116, 119, 120, 121, 123, 124, 127, 131
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OFFSET

1,2


COMMENTS

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).


LINKS



EXAMPLE

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


MATHEMATICA

Select[Range[150], Mod[#1 ((#1 + 1)/2)  DivisorSigma[1, #1], 2] == 0 & ]
Select[Range[150], EvenQ[(#(#+1))/2DivisorSigma[1, #]]&] (* Harvey P. Dale, Oct 21 2018 *)


PROG

(PARI) isok(n) = (sum(k=1, n1, k*((n % k) != 0)) % 2) == 0; \\ Michel Marcus, Dec 11 2016


CROSSREFS

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


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



