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A108957 Values of n such that n - 2^k is deficient for all 1 <= 2^k < n. 2

%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

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)