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

4, 5, 6, 8, 10, 13, 14, 16, 17, 21, 22, 26, 29, 30, 32, 33, 34, 36, 37, 38, 41, 42, 45, 46, 53, 54, 57, 58, 61, 62, 64, 65, 66, 69, 70, 72, 73, 74, 77, 78, 82, 85, 86, 89, 90, 93, 94, 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

Offset: 1

Author

Ilya Gutkovskiy, Dec 10 2016

Keywords

• nonn
• easy

Comments

Numbers n such that A000035(A024816(n)) = 1 or A000035(A000217(n)-A000203(n)) = 1.

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).

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000035, A000203, A000217, A014601, A024816, A028982, A028983, A042963, A053868, A053869, A279064.

Programs

Maple

filter:= n -> evalb(n+1 mod 4 <= 1) = (issqr(n) or issqr(n/2)):
select(filter, [$1..200]); # Robert Israel, Dec 11 2016

Mathematica

Select[Range[150], Mod[#1 ((#1 + 1)/2) - DivisorSigma[1, #1], 2] == 1 & ]
Select[Range[150],OddQ[Total[Complement[Range[#],Divisors[#]]]]&] (* Harvey P. Dale, Jul 29 2024 *)