A223608 Numbers n whose deficiency is 18: sigma(n) - 2*n = -18.

19, 33, 105, 33705, 33624064, 2199041081344

Offset: 1

Author

Donovan Johnson, Mar 23 2013

Keywords

• nonn
• more

Comments

Suggested by N. J. A. Sloane and Robert G. Wilson v.

a(6) > 10^12.

a(7) > 10^13. - Giovanni Resta, Mar 29 2013

a(7) > 10^18. - Hiroaki Yamanouchi, Aug 21 2018

Any term x of this sequence can be combined with any term y of A223610 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable. - Timothy L. Tiffin, Sep 13 2016

Examples

			n = 33624064. sigma(n)-2*n = -18.
		

Crossrefs

Cf. A000203, A033879, A223610 (abundance 18).

Programs

Magma

[n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq -18]; // Vincenzo Librandi, Sep 14 2016

Mathematica

Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == - 18 &] (* Vincenzo Librandi, Sep 14 2016 *)

PARI

for(n=1, 10^8, if(sigma(n)-2*n==-18, print1(n ", ")))

Extensions

a(6) from Giovanni Resta, Mar 29 2013