%I #8 Sep 21 2019 08:25:57
%S 2,3,4,5,6,9,11,12,15,17,18,23,27,33,35,39,45,47,51,53,54,59,63,65,66,
%T 69,75,77,83,87,93,95,99,107,111,117,119,123,125,126,129,131,135,137,
%U 138,143,147,149,150,153,155,159,165,167,171,173,174,179,183,185,186
%N Values of n such that n - 2^k is deficient for all 1 <= 2^k < n.
%C Conjectures: a. Sequence is infinite. b. There are infinitely many consecutive pairs, such as (5:6), (11:12), (17:18), (53:54), ... (204005:204006).
%H Amiram Eldar, <a href="/A108957/b108957.txt">Table of n, a(n) for n = 1..10000</a>
%e 53 is a term because 52, 51, 49, 45, 37 and 21 are all deficient numbers.
%t aQ[n_] := AllTrue[n - 2^Range[0, Floor[Log2[n]]], # == 0 || DivisorSigma[1, #] < 2 # &]; Select[Range[2, 186], aQ] (* _Amiram Eldar_, Sep 21 2019 *)
%Y Cf. A005100, A039669.
%K easy,nonn
%O 1,1
%A _Jason Earls_, Jul 22 2005