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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.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Aug 27 2015
STATUS
approved