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A214547
Deficient numbers for which the (absolute value of) abundance is not a divisor.
1
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
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
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