

A094783


Numbers n such that, for all m < n, d_i(n) <= d_i(m) for i=1 to Min(d(n),d(m)), where d_i(n) denotes the ith smallest divisor of n.


6



1, 2, 4, 6, 12, 24, 48, 60, 120, 240, 360, 1680, 2520, 5040, 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 720720, 1441440, 2162160, 3603600, 7207200, 10810800, 122522400, 183783600, 2327925600, 3491888400, 80313433200
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OFFSET

1,2


COMMENTS

The function d(n) (A000005) is the number of divisors of n.
The defining criterion for this sequence is a sufficient, but not necessary, condition for membership in A095849.
Subsequence of A002182.  David Wasserman, Jun 28 2007
Why is 720 not in the sequence? The divisors of 360 begin 1,2,3,4,5,6,8,9,10,12,15,18 and the divisors of 720 begin 1,2,3,4,5,6,8,9,10,12,15,16.  J. Lowell, Aug 23 2007 [Answer from Don Reble, Sep 11 2007: 720 is precluded by 420. (1,2,3,4,5,6,7,10,12,14,15,20,21,...)]
Conjecture: If n is in this sequence, then so is the smallest number with n divisors. (This conjecture is definitely false for A002182 (n=840) and A019505 (n=240.)  J. Lowell, Jan 24 2008


LINKS

Table of n, a(n) for n=1..33.
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau Of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 844.
J. Britton, Perfect Number Analyzer.
Wikipedia, Table of divisors.


EXAMPLE

As n increases, the positive integer n=6 sets or ties the existing records for smallest first, second and thirdsmallest divisors (1, 2 and 3), as well as for its fourthsmallest (6). Since no smaller integer has more than three divisors, 6 satisfies the requirement for this sequence.


CROSSREFS

Cf. A123258.
Sequence in context: A135614 A115387 A095849 * A058764 A087009 A168263
Adjacent sequences: A094780 A094781 A094782 * A094784 A094785 A094786


KEYWORD

nonn


AUTHOR

Matthew Vandermast, Jun 10 2004


EXTENSIONS

More terms from David Wasserman, Jun 28 2007
Definition corrected by Ray Chandler, May 05 2008


STATUS

approved



