OFFSET
1,1
COMMENTS
Numbers n whose abundance is -12. No other terms up to n=100,000,000. - Jason G. Wurtzel, Aug 24 2010
a(8) > 10^12. - Donovan Johnson, Dec 08 2011
a(8) > 10^13. - Giovanni Resta, Mar 29 2013
a(10) > 10^18. - Hiroaki Yamanouchi, Aug 21 2018
a(8) <= 35184418226176 = 3.52*10^13. Indeed, for all k in A102633, the number 2^(k-1)*(2^k+11) is in this sequence. So far all terms except a(2) are of this form. For k = 23, this gives the (probably next) term 35184418226176. For k = 29, 31, 55, 71, ... this yields 144115191028645888, 2305843021024854016, 649037107316853651724695645454336, 2787593149816327892704951291908936712585216, ... which are also in this sequence. - M. F. Hasler, Apr 23 2015
Any term x = a(m) can be combined with any term y = A141545(n) to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2. Although this property is a necessary condition for two numbers to be amicable, it is not a sufficient one. So far, these two sequences have not produced an amicable pair. However, if one is ever found, then it will exhibit x-y = 12. - Timothy L. Tiffin, Sep 13 2016
EXAMPLE
a(1) = 13, since 2*13 - sigma(13) = 26 - 14 = 12. - Timothy L. Tiffin, Sep 13 2016
MATHEMATICA
lst={}; Do[If[n==Plus@@Divisors[n]-n+12, AppendTo[lst, n]], {n, 10^4}]; Print[lst];
Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == - 12 &] (* Vincenzo Librandi, Sep 14 2016 *)
PROG
(PARI) for(n=1, 10^8, if(((sigma(n)-2*n)==-12), print1(n, ", "))) \\ Jason G. Wurtzel, Aug 24 2010
(Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq -12]; // Vincenzo Librandi, Sep 14 2016
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Vladimir Joseph Stephan Orlovsky, Aug 16 2008
EXTENSIONS
a(7) from Donovan Johnson, Dec 08 2011
a(8)-a(9) from Hiroaki Yamanouchi, Aug 21 2018
STATUS
approved