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A125247
Numbers n whose abundance sigma(n) - 2n = -8. Numbers n whose deficiency is 8.
16
22, 130, 184, 1012, 2272, 18904, 33664, 70564, 85936, 100804, 391612, 527872, 1090912, 17619844, 2147713024, 6800695312, 34360655872, 549759483904, 1661355408388, 28502765343364, 82994670582016, 99249696661504, 120646991405056, 431202442356004, 952413274955776
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
Cf. A033880, A088833 (abundance 8).
Sequence in context: A229375 A309923 A215626 * A249302 A095694 A233060
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