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A080372 a(n) = smallest x such that quotient d(x)/d(x+1) equals n, where d()=A000005, the number of divisors. 2
2, 6, 12, 30, 112, 60, 192, 210, 180, 240, 13312, 420, 12288, 2112, 1008, 1320, 2162688, 1800, 786432, 2160, 4800, 15360, 62914560, 2520, 6480, 61440, 6300, 8640, 3489660928, 12240, 3221225472, 7560, 64512, 1376256, 58320, 12600, 206158430208, 8650752, 184320, 15120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(41) > 10^12. - Donovan Johnson, Sep 02 2013

LINKS

Table of n, a(n) for n=1..40.

Donovan Johnson, All 433 terms <= 10^12

FORMULA

a(n)=Min{x : d[x]/d[x+1]=n}

EXAMPLE

n = 17: a(17) = 2162688 = m, d(m) = 68, d(m+1) = 4, quotient = 17.

MATHEMATICA

t = Table[ 0, {50}]; Do[ s = DivisorSigma[0, n] / DivisorSigma[0, n+1]; If[ s < 51 && t[[s]] == 0, t[[s]] = n], {n, 1, 45000000}]; t

CROSSREFS

Cf. A000005, A080371.

Sequence in context: A320664 A022916 A073949 * A163087 A000650 A304961

Adjacent sequences:  A080369 A080370 A080371 * A080373 A080374 A080375

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 24 2003

EXTENSIONS

More terms from Robert G. Wilson v, Feb 27 2003

The sequence continues: ?, 2520, 6480, 61440, 6300, 8640, ?, 12240, ?, 7560, 64512, 1376256, 58320, 12600, ?, 8650752 ...

a(23), a(29) and a(31) from Donovan Johnson, Jun 02 2010

a(37), a(39)-a(40) from Donovan Johnson, Sep 02 2013

STATUS

approved

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Last modified October 24 01:20 EDT 2018. Contains 316541 sequences. (Running on oeis4.)