A237046 Numbers n such that sigma(n) < 2n-1.

3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97, 98, 99, 101

Offset: 1

Author

Omar E. Pol, Feb 19 2014

Keywords

• nonn
• easy

Comments

Numbers n such that A235796(n) > 0.

Complement of A103288.

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).

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

Select[Range[120],DivisorSigma[1,#]<2#-1&] (* Harvey P. Dale, Sep 12 2018 *)

PARI

s=[]; for(n=1, 200, if(sigma(n)<2*n-1, s=concat(s,n))); s \\ Colin Barker, Feb 20 2014