A180734 Numbers the absolute value of whose deficiency is a deficient number.

1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 14, 16, 17, 18, 20, 21, 22, 23, 25, 26, 27, 32, 34, 35, 36, 38, 39, 40, 44, 47, 49, 50, 53, 55, 56, 57, 58, 59, 63, 64, 65, 68, 70, 72, 74, 75, 77, 80, 81, 82, 83, 85, 88, 92, 93, 94, 98, 100, 104, 106, 107, 108, 110, 115, 116, 117, 119, 121, 122, 125, 128

Offset

1,2

Comments

Companion sequences are numbers the absolute value of whose deficiency is a perfect number, numbers the absolute value of whose deficiency is an abundant number. Every nonnegative integer is in one of these three sequences.

Links

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

Formula

{n such that A033879(n) is in A005100} = {n such that A005843(n)-A000203(n) is in A005100} = {n such that sigma (| 2*n-sigma(n) | ) < 2*(A033879(n))} = {n such that sigma (| 2*n-sigma(n) | ) < 2*(2*n-sigma(n)))}.

Example

a(1) = 1 because the deficiency of 1 is 1, and 1 is itself a deficient number.
a(10) = 12 because the deficiency of 12 is -4 and  | -4 | = 4 is a deficient number.
7 is not in the sequence because the deficiency of 7 is 6, and 6 is a perfect number.
13 is not in the sequence because the deficiency of 13 is 12, and 12 is an abundant number.

Mathematica

Deficiency[n_] := 2 n - DivisorSigma[1, n]; Select[Range[150], Deficiency[Abs[Deficiency[#]]] > 0 &]

Crossrefs

Cf. A000203, A000396, A005100, A005101, A005843, A033630, A033879.

Sequence in context: A037471 A080401 A288666 * A031482 A047369 A004827

Adjacent sequences: A180731 A180732 A180733 * A180735 A180736 A180737

Keyword

nonn,easy

Author

Jonathan Vos Post, Jan 21 2011

Status

approved