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A127666 Odd infinitary abundant numbers. 8
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

REFERENCES

Cohen, Graeme L.; On an Integer's Infinitary Divisors, Mathematics of Computation, Vol. 54, No. 189. (1990), pp. 395-411.

LINKS

Table of n, a(n) for n=1..34.

J. O. M. Pedersen, Tables of Aliquot Cycles.

FORMULA

Odd values of n for which A126168(n)>n.

EXAMPLE

a(5)=16065 because 16065 is the fifth odd number that is exceeded by the sum of its proper infinitary divisors.

MATHEMATICA

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[ # ]># &]

CROSSREFS

Cf. A126168, A127661.

Sequence in context: A188263 A188342 A109729 * A133818 A112491 A133353

Adjacent sequences:  A127663 A127664 A127665 * A127667 A127668 A127669

KEYWORD

nonn

AUTHOR

Ant King, Jan 26 2007

STATUS

approved

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Last modified April 19 21:10 EDT 2014. Contains 240777 sequences.