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A348005
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Positive even integers with an even number of even divisors.
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2
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4, 6, 10, 12, 14, 16, 20, 22, 24, 26, 28, 30, 34, 36, 38, 40, 42, 44, 46, 48, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156
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OFFSET
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1,1
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COMMENTS
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These terms are exactly the even numbers in A183300.
Complement of A001105 relative to the positive even integers (A005843 \ {0}).
Note that odd integers with an odd number of odd divisors are the odd squares (A016754).
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LINKS
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FORMULA
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EXAMPLE
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The divisors of 14 are {1, 2, 7, 14}, two of them: 2 and 14 are even, hence 14 is a term.
The divisors of 16 are {1, 2, 4, 8, 16}, four of them: 2, 4, 8 and 16 are even, hence 16 is another term.
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MAPLE
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filter:= q -> irem(q, 2) = 0 and sqrt(q/2) <> floor(sqrt(q/2)) : select(filter, [$1..156]);
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MATHEMATICA
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m = 9; 2 * Complement[Range[m^2], Range[m]^2] (* Amiram Eldar, Oct 02 2021 *)
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PROG
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(PARI) isok(k) = !(k % 2) && !(sumdiv(k, d, !(d % 2)) % 2); \\ Michel Marcus, Oct 05 2021
(Python)
from math import isqrt
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CROSSREFS
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-------------------------------------------------------------------------
| Integers with | an even number of ... | an odd number of ... |
-------------------------------------------------------------------------
-------------------------------------------------------------------------
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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