|
|
A141550
|
|
Numbers n whose deficiency is 14.
|
|
7
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
a(6) <= b(38) = 37778931864743868104704 = 3.77789*10^22, since b(k) = 2^(k-1)*(2^k+13) is in this sequence for all k in A102634, i.e., 2^k+13 is prime. All known terms except a(1) = 27 are of this form: a(2..5) = b(k) with k = 2, 4, 8, 20, and k = 38 yields the next larger term of this form. - M. F. Hasler, Jul 18 2016
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
|
|
|
EXAMPLE
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|