A141549 Numbers k whose deficiency is 12: 2k - sigma(k) = 12.

13, 45, 76, 688, 8896, 133888, 537051136, 35184418226176, 144115191028645888, 2305843021024854016

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2008

Keywords

• nonn
• hard
• more

Comments

Numbers n whose abundance is -12. No other terms up to n=100,000,000. - Jason G. Wurtzel, Aug 24 2010

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 = 55, 71, this yields terms 649037107316853651724695645454336, 2787593149816327892704951291908936712585216. - M. F. Hasler, Apr 23 2015; edited by Max Alekseyev, May 27 2025

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

a(11) > 10^20. - Max Alekseyev, May 27 2025

Examples

			a(1) = 13, since 2*13 - sigma(13) = 26 - 14 = 12. - _Timothy L. Tiffin_, Sep 13 2016
		

Crossrefs

Cf. A000203, A033880, A005100; A191363 (deficiency 2), A125246 (deficiency 4), A141548 (deficiency 6), A125247 (deficiency 8), A101223 (deficiency 10), A141550 (deficiency 14), A125248 (deficiency 16), A223608 (deficiency 18), A223607 (deficiency 20); A141545 (abundance 12).

Programs

Magma

[n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq -12]; // Vincenzo Librandi, Sep 14 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 *)

PARI

for(n=1, 10^8, if(((sigma(n)-2*n)==-12), print1(n, ", "))) \\ Jason G. Wurtzel, Aug 24 2010

Extensions

a(7) from Donovan Johnson, Dec 08 2011

a(8)-a(9) from Hiroaki Yamanouchi, Aug 21 2018

a(10) from Max Alekseyev, May 27 2025