

A128700


Highly abundant numbers with an odd divisor sum.


3



1, 2, 4, 8, 16, 18, 36, 72, 144, 288, 1800, 3600, 7200
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OFFSET

1,2


COMMENTS

Alaoglu and Erdős showed that 7200 is the largest highly abundant number with all the exponents of its prime factors occurring to powers greater than unity. It follows that the sequence of highly abundant numbers with an odd divisor sum is finite and is bounded above by 7200. Accordingly, this is the complete sequence of such integers.


LINKS

Table of n, a(n) for n=1..13.
L. Alaoglu and P. Erdős, On highly composite and similar numbers, Trans. Amer. Math. Soc., 56 (1944), 448469.
Wikipedia, Highly Abundant Numbers.


FORMULA

The highly abundant numbers are those integers for which sigma(n) > sigma(m) for all m < n (A002093). This sequence contains those elements of A002093 that have an odd divisor sum.


EXAMPLE

The fifth highly abundant number with an odd divisor sum is 15. Hence a(5)=15.


MATHEMATICA

hadata1=FoldList[Max, 1, Table[DivisorSigma[1, n], {n, 2, 7200}]]; data1=Flatten[Position[hadata1, #, 1, 1]&/@Union[hadata1]]; Select[data1, OddQ[DivisorSigma[1, # ]] &]


CROSSREFS

Cf. A002093, A000203.
Sequence in context: A316900 A076057 A133809 * A212204 A184986 A018547
Adjacent sequences: A128697 A128698 A128699 * A128701 A128702 A128703


KEYWORD

easy,full,nice,nonn,fini


AUTHOR

Ant King, Mar 28 2007


STATUS

approved



