

A141550


Numbers n whose deficiency is 14.


7




OFFSET

1,1


COMMENTS

a(6) > 10^12.  Donovan Johnson, Dec 08 2011
a(6) > 10^13.  Giovanni Resta, Mar 29 2013
a(6) > 10^18.  Hiroaki Yamanouchi, Aug 21 2018
a(6) <= b(38) = 37778931864743868104704 = 3.77789*10^22, since b(k) = 2^(k1)*(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

Table of n, a(n) for n=1..5.


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

Cf. A000203, A033880, A005100; A191363 (deficiency 2), A125246 (deficiency 4), A141548 (deficiency 6), A125247 (deficiency 8), A101223 (deficiency 10), A141549 (deficiency 12), A125248 (deficiency 16); A141546 (abundance 14).
Sequence in context: A309063 A088499 A058902 * 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


STATUS

approved



