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

1,2

Links

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

Example

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

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 *)

Crossrefs

Cf. A000203, A024816, A055008, A058075.

Sequence in context: A080064 A329609 A340784 * A243188 A117570 A337816

Adjacent sequences: A260960 A260961 A260962 * A260964 A260965 A260966

Keyword

nonn,easy

Author

Paolo P. Lava, Aug 27 2015

Status

approved