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

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, 69, 75, 77, 83, 87, 93, 95, 99, 107, 111, 117, 119, 123, 125, 126, 129, 131, 135, 137, 138, 143, 147, 149, 150, 153, 155, 159, 165, 167, 171, 173, 174, 179, 183, 185, 186

Offset: 1

Author

Jason Earls, Jul 22 2005

Keywords

• easy
• nonn

Comments

Conjectures: a. Sequence is infinite. b. There are infinitely many consecutive pairs, such as (5:6), (11:12), (17:18), (53:54), ... (204005:204006).

Examples

			53 is a term because 52, 51, 49, 45, 37 and 21 are all deficient numbers.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005100, A039669.

Programs

Mathematica

aQ[n_] := AllTrue[n - 2^Range[0, Floor[Log2[n]]], # == 0 || DivisorSigma[1, #] < 2 # &]; Select[Range[2, 186], aQ] (* Amiram Eldar, Sep 21 2019 *)