

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


PROG

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


CROSSREFS

Cf. A005100, A033880, A214408.
Sequence in context: A329405 A194391 A081534 * A097218 A196546 A231773
Adjacent sequences: A214544 A214545 A214546 * A214548 A214549 A214550


KEYWORD

nonn,easy


AUTHOR

Jonathan Vos Post, Jul 20 2012


EXTENSIONS

Given terms doublechecked with the PARI script by M. F. Hasler, Jul 21 2012


STATUS

approved



