A260963 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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 *)