A223610 Numbers k whose abundance is 18: sigma(k) - 2*k = 18.

208, 6976, 8415, 31815, 351351, 2077696, 20487159, 159030135, 536559616, 2586415095, 137433972736, 2199003332608, 2305842988812599296

Offset: 1

Author

Donovan Johnson, Mar 23 2013, at suggestion of N. J. A. Sloane and Robert G. Wilson v

Keywords

• nonn
• more

Comments

Any term x of this sequence can be combined with any term y of A223608 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

Every number of the form 2^(j-1)*(2^j - 19), where 2^j - 19 is prime, is a term (cf. A096819). - Jon E. Schoenfield, Jun 02 2019

Examples

			For k = 159030135, sigma(k) - 2*k = 18.
		

Crossrefs

Cf. A000203, A033880, A096819, A223608 (deficiency 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(12) from Giovanni Resta, Mar 29 2013

a(13) from Jon E. Schoenfield confirmed and added by Max Alekseyev, Jun 03 2025