A237046 - OEIS

%I #23 Sep 12 2018 17:52:52

%S 3,5,7,9,10,11,13,14,15,17,19,21,22,23,25,26,27,29,31,33,34,35,37,38,

%T 39,41,43,44,45,46,47,49,50,51,52,53,55,57,58,59,61,62,63,65,67,68,69,

%U 71,73,74,75,76,77,79,81,82,83,85,86,87,89,91,92,93,94,95,97,98,99,101

%N Numbers n such that sigma(n) < 2n-1.

%C Numbers n such that A235796(n) > 0.

%C Complement of A103288.

%C If the only least-deficient numbers are the powers of 2 (which is an open problem) then the union of A000079 and A023196 and this sequence gives A000027 (see also A103288).

%e 10 is in the sequence because the sum of divisors of 10 is less than (2*10 - 1). The sum of divisors of 10 is 1 + 2 + 5 + 10 = 18 and 2*10 - 1 = 19.

%t Select[Range[120],DivisorSigma[1,#]<2#-1&] (* _Harvey P. Dale_, Sep 12 2018 *)

%o (PARI) s=[]; for(n=1, 200, if(sigma(n)<2*n-1, s=concat(s,n))); s \\ _Colin Barker_, Feb 20 2014

%Y Cf. A000203, A005100, A023196, A033879, A103288, A196020, A235796, A236104.

%K nonn,easy

%O 1,1

%A _Omar E. Pol_, Feb 19 2014