1,1

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

Contains 2^(k-1)*(2^k+17) for k in A057200. In particular, a(8) <= 2^80*(2^81+17) = 2923003274661805836407390217171499488007835090944. - Max Alekseyev, Oct 18 2025

a(8) > 10^22. - Max Alekseyev, Jan 30 2026

n = 33624064. sigma(n)-2*n = -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), A223610 (k=18), A223611 (k=20), A223612 (k=22), A223613 (k=24), A275701 (k=26), A175989 (k=32), A275996 (k=64), A292626 (k=128).

Cf. A000203, A033879, A057200.

Sequence in context: A372427 A362410 A106527 * A146438 A146571 A235869

Adjacent sequences: A223605 A223606 A223607 * A223609 A223610 A223611

nonn,more

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

a(6) from Giovanni Resta, Mar 29 2013

a(7) from Max Alekseyev, Oct 18 2025

approved