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Search: id:A127666
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| A127666 |
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Odd infinitary abundant numbers. |
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+0
9
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| 945, 10395, 12285, 15015, 16065, 17955, 19305, 19635, 21735, 21945, 23205, 23625, 25245, 25935, 26565, 27405, 28215, 28875, 29295, 29835, 31395, 33345, 33495, 33915, 34125, 34155, 34965, 35805, 37125, 38745, 39585, 40635, 41055, 42315
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This is also the sequence of odd integers whose infinitary aliquot sequences initially increase. Based on empirical evidence (up to 10 million), this applies to only about 0.1% of odd integers.
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REFERENCES
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Cohen, Graeme L.; On an Integer's Infinitary Divisors, Mathematics of Computation, Vol. 54, No. 189. (1990), pp. 395-411.
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LINKS
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J. O. M. Pedersen, Tables of Aliquot Cycles.
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FORMULA
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Odd values of n for which A126168(n)>n.
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EXAMPLE
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a(5)=16065 because 16065 is the fifth odd number that is exceeded by the sum of its proper infinitary divisors.
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MATHEMATICA
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ExponentList[n_Integer, factors_List]:={#, IntegerExponent[n, # ]}&/@factors; InfinitaryDivisors[1]:={1}; InfinitaryDivisors[n_Integer?Positive]:=Module[ { factors=First/@FactorInteger[n], d=Divisors[n] }, d[[Flatten[Position[ Transpose[ Thread[Function[{f, g}, BitOr[f, g]==g][ #, Last[ # ]]]&/@ Transpose[Last/@ExponentList[ #, factors]&/@d]], _?(And@@#&), {1}]] ]] ] Null; properinfinitarydivisorsum[k_]:=Plus@@InfinitaryDivisors[k]-k; Select[Range[1, 50000, 2], properinfinitarydivisorsum[ # ]># &]
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CROSSREFS
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Cf. A126168, A127661.
Sequence in context: A006038 A127667 A109729 this_sequence A133818 A112491 A133353
Adjacent sequences: A127663 A127664 A127665 this_sequence A127667 A127668 A127669
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KEYWORD
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nonn
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AUTHOR
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Ant King (mathstutoring(AT)ntlworld.com), Jan 26 2007
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