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Search: id:A006037
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| 70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792, 10990, 11410, 11690, 12110, 12530, 12670, 13370, 13510, 13790, 13930, 14770, 15610, 15890, 16030, 16310, 16730, 16870, 17272, 17570, 17990, 18410, 18830, 18970, 19390, 19670
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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There are no odd weird numbers < 10^17. - Robert A. Hearn (rah(AT)ai.mit.edu), May 25 2005
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REFERENCES
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S. Benkoski, "Are All Weird Numbers Even?", Problem E2308, Amer. Math. Monthly, 79 (1972), 774.
S. J. Benkoski and P. Erdos, On weird and pseudoperfect numbers, Math. Comp., 28 (1974), 617-623.
R. K. Guy, Unsolved Problems in Number Theory, B2.
H. J. Hindin, Quasipractical numbers, IEEE Communications Magazine, March 1980, pp. 41-45.
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 70, p. 24, Ellipses, Paris 2008.
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LINKS
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M. F. Hasler, Table of n, a(n) for n=1,...,1000.
Bj"orn B"ottcher, Weird Numbers: Definition
K. Uhland, Weird Numbers
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Wikipedia, Weird number
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MATHEMATICA
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(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) fQ[n_] := Block[{d, l, t, i}, If[ DivisorSigma[1, n] > 2n && Mod[n, 6] != 0, d = Take[Divisors[n], {1, -2}]; l = 2^Length[d]; t = Table[ NthSubset[j, d], {j, l - 1}]; i = 1; While[i < l && Plus @@ t[[i]] != n, i++ ]]; If[i == l, True, False]]; Select[ Range[ 20000], fQ[ # ] &] (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 20 2005)
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PROGRAM
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(PARI) isA006037(n, d=0)={ local(t); /* if d is not given, return nonzero iff n is weird ; if d is given, return nonzero iff n is not the sum of a subset of d */ if( !d, sigma(n)<=2*n & return /*must be abundant*/; d=vecextract(divisors(n), "^-1")); setsearch( Set(d), n ) & return /* equal to one element of d */; while( d[ #d]>n, d=vecextract(d, "^-1")); n >= (t = sum(i=1, #d, d[i])) & return( n-t /* nonzero if n>t */ ); n > d[ #d] & ! isA006037( n - d[ #d], d=vecextract( d, "^-1" )) & return; isA006037( n, d )}
(PARI) t=0; A006037=vector(1000, i, until( isA006037(t+=2), )= ; t) \\ - M. F. Hasler, Mar 30 2008
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CROSSREFS
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Cf. A002975, A005101, A005835, A005100, A138850; A087167.
Sequence in context: A060541 A104475 A027804 this_sequence A002975 A061170 A125114
Adjacent sequences: A006034 A006035 A006036 this_sequence A006038 A006039 A006040
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KEYWORD
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nonn,nice
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AUTHOR
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njas
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EXTENSIONS
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More terms from Jud McCranie (j.mccranie(AT)comcast.net), Oct 21 2001
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