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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.

%I A260963 #12 Aug 01 2019 04:10:54
%S A260963 1,4,9,10,16,21,22,25,34,36,46,49,57,58,64,70,81,82,85,93,94,100,106,
%T A260963 118,121,129,130,133,142,144,154,166,169,178,201,202,205,214,217,225,
%U A260963 226,237,238,250,253,256,262,265,274,289,298,301,309,310,322,324,325
%N 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.
%H A260963 Paolo P. Lava, <a href="/A260963/b260963.txt">Table of n, a(n) for n = 1..10000</a>
%e A260963 sigma(10) = 18, 10*11/2 - sigma(10) = 55 - 18 = 37 and gcd(18,37) = 1 because 18 = 2*9 and 37 is prime.
%p A260963 with(numtheory): P:=proc(q) local n; for n from 1 to q do
%p A260963 if gcd(sigma(n),n*(n+1)/2-sigma(n))=1 then print(n); fi; od; end: P(10^9);
%t A260963 Select[Range@ 360, GCD[DivisorSigma[1, #], # (# + 1)/2 - DivisorSigma[1, #]] == 1 &] (* _Michael De Vlieger_, Aug 27 2015 *)
%Y A260963 Cf. A000203, A024816, A055008, A058075.
%K A260963 nonn,easy
%O A260963 1,2
%A A260963 _Paolo P. Lava_, Aug 27 2015