1,1

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

Max A. Alekseyev, Computing bounded solutions to linear Diophantine equations with the sum of divisors, arXiv:2601.17832 [math.NT], 2026. See p. 9.

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

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 ", ")))

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

Deficiency k: A191363 (k=2), A125246 (k=4), A141548 (k=6), A125247 (k=8), A101223 (k=10), A141549 (k=12), A141550 (k=14), A125248 (k=16), A223608 (k=18), A223607 (k=20), A223606 (k=22), A385255 (k=24), A275702 (k=26), A387352 (k=32), A175730 (k=42), A101259 (k=54), A275997 (k=64).

Abundance k: A088831 (k=2), A088832 (k=4), A087167 (k=6), A088833 (k=8), A223609 (k=10), A141545 (k=12), A141546 (k=14), A141547 (k=16), A223611 (k=20), A223612 (k=22), A223613 (k=24), A275701 (k=26), A175989 (k=32), A275996 (k=64), A292626 (k=128).

Cf. A000203, A033880, A096819.

Sequence in context: A231111 A339762 A223252 * A184276 A268091 A209300

Adjacent sequences: A223607 A223608 A223609 * A223611 A223612 A223613

nonn,more

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

a(12) from Giovanni Resta, Mar 29 2013

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

a(14) from Max Alekseyev, Oct 17 2025

approved