A141550 Numbers n whose deficiency is 14.

27, 34, 232, 34432, 549762629632, 37778931864743868104704

Offset

1,1

Comments

2^(k-1)*(2^k+13) is in this sequence for all k in A102634, i.e., when 2^k+13 is prime. All known terms except a(1) = 27 are of this form. - M. F. Hasler, Jul 18 2016 [Updated by Max Alekseyev, Oct 20 2025]

Any term x of this sequence can be combined with any term y of A141546 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

Links

Table of n, a(n) for n=1..6.

Example

a(1) = 27, since 2*27 - sigma(27) = 54 - 40 = 14. - Timothy L. Tiffin, Sep 13 2016

Mathematica

lst={}; Do[If[n==Plus@@Divisors[n]-n+14, AppendTo[lst, n]], {n, 10^4}]; Print[lst];
Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == - 14 &] (* Vincenzo Librandi, Sep 14 2016 *)

Prog

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

Crossrefs

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, A033880, A005100, A102634.

Sequence in context: A088499 A058902 A342844 * A032584 A072492 A164376

Adjacent sequences: A141547 A141548 A141549 * A141551 A141552 A141553

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2008

Extensions

a(5) from Donovan Johnson, Dec 08 2011

a(6) from M. F. Hasler confirmed and added by Max Alekseyev, Oct 20 2025

Status

approved