

A188597


Odd deficient numbers whose abundancy is closer to 2 than any smaller odd deficient number.


7



1, 3, 9, 15, 45, 105, 315, 1155, 26325, 33705, 449295, 1805475, 10240425, 13800465, 16029405, 16286445, 21003885, 32062485, 132701205, 594397485, 815634435, 29169504045, 40833636525, 295612416135, 636988686495, 660733931655, 724387847085, 740099543085, 1707894294975, 4439852974095, 7454198513685
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OFFSET

1,2


COMMENTS

The abundancy of a number n is defined to be A(n) = sigma(n)/n. Deficient numbers have an abundancy less than 2. This sequence has terms in common with A171929. Sequence A188263, which deals with abundant numbers, approaches 2 from above. The similar sequence for even numbers consists of the powers of 2.
a(29) > 10^12.  Donovan Johnson, Apr 08 2011
This sequence is finite iff there is an odd perfect number (which would have abundancy 2). Otherwise, one has always a subsequent term a(n+1) <= a(n)*p where p is the smallest prime not dividing a(n) and larger than 1/(2/A(a(n))1). Indeed, such an a(n)*p is still deficient but has abundancy larger than a(n), thus closer to 2.  M. F. Hasler, Feb 22 2017
From M. F. Hasler, Jan 25 2020: (Start)
The upper bounds a(n)*p mentioned above are often terms of the sequence, but not the subsequent but a later one: e.g., 9*5 = 45, 15*7 = 105, 45*7 = 315, 105*11 = 1155, 315*107 = 33705, 1155*389 = 449295, 26325*389 = 10240425, ...
Is 9 the largest term not divisible by 15? After 45, only 7 of the listed 315 terms are not multiples of 7: is this subsequence finite? (End)


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..31 (terms < 10^13)


MATHEMATICA

k = 1; minDiff = 1; Join[{k}, Table[k = k + 2; While[abun = DivisorSigma[1, k]/k; 2  abun > minDiff  abun => 2, k = k + 2]; minDiff = 2  abun; k, {10}]]


CROSSREFS

Cf. A171929 (odd numbers whose abundancy is closer to 2 than any smaller odd number).
Sequence in context: A119239 A140864 A171929 * A330815 A338611 A329420
Adjacent sequences: A188594 A188595 A188596 * A188598 A188599 A188600


KEYWORD

nonn


AUTHOR

T. D. Noe, Apr 05 2011


EXTENSIONS

a(22)a(28) from Donovan Johnson, Apr 08 2011


STATUS

approved



