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%I #30 Apr 07 2024 09:09:23
%S 3,5,7,9,11,13,14,15,17,19,21,22,23,25,26,27,29,31,33,34,35,37,38,39,
%T 41,43,45,46,47,49,50,51,52,53,55,57,58,59,61,62,63,65,67,68,69,71,73,
%U 74,75,76,77,79,81,82,83,85,86,87,89,91,92,93,94,95,97,98,99,101,103,105,106
%N Deficient numbers for which the (absolute value of) abundance is not a divisor.
%C This is to A214408 as deficient numbers are to abundant numbers.
%C Differs from A097218, which does not contain 105, for example.
%C 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
%H Robert Israel, <a href="/A214547/b214547.txt">Table of n, a(n) for n = 1..10000</a>
%F Terms A005100(n) such that |A033880(A005100(n))| does not divide A005100(n).
%e 7 is in the sequence because 7 is deficient, and its abundance is -6, and |-6| = 6 does not divide 7.
%p filter:= proc(n) local t;
%p t:= 2*n-numtheory:-sigma(n);
%p t > 0 and n mod t <> 0
%p end proc:
%p select(filter, [$1..200]); # _Robert Israel_, Nov 13 2019
%t q[n_] := Module[{def = 2*n - DivisorSigma[1, n]}, def > 0 && !Divisible[n, def]]; Select[Range[120], q] (* _Amiram Eldar_, Apr 07 2024 *)
%o (PARI) is_A214547(n)={sigma(n)<2*n & n%(2*n-sigma(n))} \\ _M. F. Hasler_, Jul 21 2012
%Y Cf. A005100, A033880, A060326, A097218, A214408.
%K nonn,easy
%O 1,1
%A _Jonathan Vos Post_, Jul 20 2012
%E Given terms double-checked with the PARI script by _M. F. Hasler_, Jul 21 2012
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