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

1,1

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

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A194391 A347468 A081534 * A097218 A196546 A371179

Adjacent sequences: A214544 A214545 A214546 * A214548 A214549 A214550

Keyword

nonn,easy

Author

Jonathan Vos Post, Jul 20 2012

Extensions

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

Status

approved