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A177712
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Even numbers that have a nontrivial odd divisor.
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6
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6, 10, 12, 14, 18, 20, 22, 24, 26, 28, 30, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 130, 132, 134, 136, 138, 140
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OFFSET
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1,1
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COMMENTS
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Numbers which can be expressed as a sum of a set of positive consecutive even numbers: sum_{i=m..m+k} A005843(i), m>=1, k>=1.
Differs from A054741, which contains 105 for example.
These are the numbers that are not free of odd prime factors, but are not odd. Compare with A051144, nonsquarefree nonsquares. The self-inverse function defined by A225546 maps the members of either set 1:1 onto the other set. - Peter Munn, Jul 31 2020 with edit Feb 14 2022
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LINKS
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FORMULA
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EXAMPLE
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6=2+4. 10=4+6. 12=2+4+6. 14=6+8. 18=4+6+8. 20=2+4+6+8. 22=10+12. 24=6+8+10.
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MATHEMATICA
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z=200; lst={}; Do[c=a; Do[c+=b; If[c<=2*z, AppendTo[lst, c]], {b, a-2, 1, -2}], {a, 2, z, 2}]; Union@lst
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PROG
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(PARI) isA177712(n) = (!(n%2)&&(0<#select(x -> x%2, factor(n)[, 1]))); \\ Antti Karttunen, Jul 31 2020
(PARI) isA177712(n) = (!(n%2)&&bitand(n, n-1)); \\ Antti Karttunen, Jul 31 2020
(Python)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Definition moved into a comment by R. J. Mathar, Aug 15 2010
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STATUS
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approved
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