A214547 Deficient numbers for which the (absolute value of) abundance is not a divisor.

3, 5, 7, 9, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97, 98, 99, 101, 103, 105, 106

Offset: 1

Author

Jonathan Vos Post, Jul 20 2012

Keywords

• nonn
• easy

Comments

This is to A214408 as deficient numbers are to abundant numbers.

Differs from A097218, which does not contain 105, for example.

The deficient numbers which are *not* in the sequence are 2, 4, 8, 10, 16, 32, 44, 64, 128, 136, 152, 184, 256, 512, 752, 884, 1024, 2048, 2144, 2272, 2528, 4096, 8192, 8384, 12224, 16384, 17176, 18632, 18904, 32768, 32896, 33664, ... the union of powers of 2 and the terms of A060326. - M. F. Hasler, Jul 21 2012

Examples

			7 is in the sequence because 7 is deficient, and its abundance is -6, and |-6| = 6 does not divide 7.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005100, A033880, A060326, A097218, A214408.

Programs

Maple

filter:= proc(n) local t;
t:= 2*n-numtheory:-sigma(n);
t > 0 and n mod t <> 0
end proc:
select(filter, [$1..200]); # Robert Israel, Nov 13 2019

Mathematica

q[n_] := Module[{def = 2*n - DivisorSigma[1, n]}, def > 0 && !Divisible[n, def]]; Select[Range[120], q] (* Amiram Eldar, Apr 07 2024 *)

PARI

is_A214547(n)={sigma(n)<2*n & n%(2*n-sigma(n))} \\ M. F. Hasler, Jul 21 2012

Formula

Terms A005100(n) such that |A033880(A005100(n))| does not divide A005100(n).

Extensions

Given terms double-checked with the PARI script by M. F. Hasler, Jul 21 2012