A260963 Numbers n such that gcd(sigma(n), n*(n+1)/2 - sigma(n)) = 1, where sigma(n) is sum of positive divisors of n.

1, 4, 9, 10, 16, 21, 22, 25, 34, 36, 46, 49, 57, 58, 64, 70, 81, 82, 85, 93, 94, 100, 106, 118, 121, 129, 130, 133, 142, 144, 154, 166, 169, 178, 201, 202, 205, 214, 217, 225, 226, 237, 238, 250, 253, 256, 262, 265, 274, 289, 298, 301, 309, 310, 322, 324, 325

Offset: 1

Author

Paolo P. Lava, Aug 27 2015

Keywords

• nonn
• easy

Examples

			sigma(10) = 18, 10*11/2 - sigma(10) = 55 - 18 = 37 and gcd(18,37) = 1 because 18 = 2*9 and 37 is prime.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A024816, A055008, A058075.

Programs

Maple

with(numtheory): P:=proc(q) local n; for n from 1 to q do
if gcd(sigma(n),n*(n+1)/2-sigma(n))=1 then print(n); fi; od; end: P(10^9);

Mathematica

Select[Range@ 360, GCD[DivisorSigma[1, #], # (# + 1)/2 - DivisorSigma[1, #]] == 1 &] (* Michael De Vlieger, Aug 27 2015 *)