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Numbers k whose deficiency is 64: 2k - sigma(k) = 64.
2

%I #29 Mar 02 2020 09:36:52

%S 134,284,410,632,1292,1628,4064,9752,12224,22712,66992,72944,403988,

%T 556544,2161664,2330528,8517632,13228352,14563832,15422912,20732792,

%U 89472632,134733824,150511232,283551872,537903104,731670272,915473696,1846850576,2149548032,2159587616

%N Numbers k whose deficiency is 64: 2k - sigma(k) = 64.

%C Any term x = a(m) in this sequence can be used with any term y in A275996 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.

%C The smallest amicable pair is (220, 284) = (A275996(2), a(2)) = (A063990(1), A063990(2)), where 284 - 220 = 64 is the abundance of 220 and the deficiency of 284.

%C The amicable pair (66928, 66992) = (A275996(7), a(11)) = (A063990(18), A063990(19)), where 66992 - 66928 = 64 is the deficiency of 66992 and the abundance of 66928.

%e a(1) = 134, since 2*134 - sigma(134) = 268 - 204 = 64.

%t Select[Range[10^7], 2 # - DivisorSigma[1, #] == 64 &] (* _Michael De Vlieger_, Jan 10 2017 *)

%o (PARI) isok(n) = 2*n - sigma(n) == 64; \\ _Michel Marcus_, Dec 30 2016

%Y Cf. A002025, A063990, A275996.

%K nonn

%O 1,1

%A _Timothy L. Tiffin_, Aug 16 2016

%E More terms from _Jinyuan Wang_, Mar 02 2020