A279064 Numbers n such that the sum of numbers less than n that do not divide n is even.

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

Offset

1,2

Comments

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

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

Harvey P. Dale, Table of n, a(n) for n = 1..2000

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A076297 A174184 A278485 * A294109 A294263 A345745

Adjacent sequences: A279061 A279062 A279063 * A279065 A279066 A279067

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Dec 10 2016

Status

approved