login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers n such that sigma(n) < 2n-1.
3

%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