1,1

Any term x of this sequence can be combined with any term y of A101223 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 - 11) for k in A096817. In particular, a(6) <= 2^77*(2^78-11). - Max Alekseyev, Jan 11 2026

Max A. Alekseyev, Computing bounded solutions to linear Diophantine equations with the sum of divisors, arXiv:2601.17832 [math.NT], 2026. See p. 9, Table 1.

Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == 10 &] (* Vincenzo Librandi, Sep 15 2016 *)

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

(Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq 10]; // Vincenzo Librandi, Sep 15 2016

Cf. A000203, A033880, A101223 (deficiency 10).

Sequence in context: A278431 A229584 A140702 * A145294 A147520 A190926

Adjacent sequences: A223606 A223607 A223608 * A223610 A223611 A223612

nonn,more

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

Edited and a(5) added by Max Alekseyev, Jan 11 2026

approved