OFFSET
1,1
COMMENTS
a(19) > 10^12. - Donovan Johnson, Dec 08 2011
a(20) > 10^13. - Giovanni Resta, Mar 29 2013
a(30) > 10^18. - Hiroaki Yamanouchi, Aug 21 2018
a(20) <= 36028797958488064 ~ 3.6*10^16. Indeed, if k is in A057195 then 2^(k-1)*A168415(k) is in this sequence, and k=28 yields this upper bound for a(20) which is in any case a term of this sequence. - M. F. Hasler, Apr 27 2015
If n is in this sequence and p a prime not dividing n, then np is abundant if and only if p < sigma(n)/8 = n/4-1. For all n=a(k) except {22, 70564, 100804, 17619844}, there is such a p near this limit, such that n*p is a primitive weird number (A002975; in A258882 for the terms mentioned in the preceding comment). - M. F. Hasler, Jul 20 2016
Any term x of this sequence can be combined with any term y of A088833 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
Is there any odd number in this sequence? Is it possible to prove the contrary? - M. F. Hasler, Feb 22 2017
LINKS
Hiroaki Yamanouchi, Table of n, a(n) for n = 1..29
EXAMPLE
The abundance of 22 = (1+2+11+22)-44 = -8
MATHEMATICA
Select[Range[10^6], DivisorSigma[1, #] - 2 # == -8 &] (* Michael De Vlieger, Jul 21 2016 *)
PROG
(PARI) for(n=1, 1000000, if(((sigma(n)-2*n)==-8), print1(n, ", ")))
(Magma) [n: n in [1..2*10^7] | (DivisorSigma(1, n)-2*n) eq - 8]; // Vincenzo Librandi, Jul 22 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jason G. Wurtzel, Nov 25 2006
EXTENSIONS
a(13)-a(15) from Klaus Brockhaus, Nov 29 2006
a(16)-a(17) from Donovan Johnson, Dec 23 2008
a(18) from Donovan Johnson, Dec 08 2011
a(19) from Giovanni Resta, Mar 29 2013
a(20)-a(25) from Hiroaki Yamanouchi, Aug 21 2018
STATUS
approved