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A019505 a(n) is smallest number with same number of divisors as 2*a(n-1). 9
1, 2, 4, 6, 12, 24, 48, 60, 120, 240, 360, 720, 1260, 2520, 5040, 10080, 20160, 27720, 55440, 110880, 221760, 332640, 665280, 1081080, 2162160, 4324320, 8648640, 17297280, 21621600, 43243200, 73513440, 147026880, 294053760, 367567200, 735134400, 1396755360, 2793510720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From J. Lowell, Mar 19 2012 and Apr 05 2012: (Start)

Conjectures:

Subsequence of A002182.

In order for n to be followed by a number less than 2n, a requirement is that the number of 2's in the prime factorization of n must not be of the form p-2 where p is a prime.

There are infinitely many values where n, 2n, and 3n are all in this sequence. (It can be proved that n, 2n, 3n, and 4n can never all be in this sequence.)

In any group of 3 consecutive terms of this sequence a,b,c at most one of the following statements is true:

The value of b is less than twice a.

The value of c is less than twice b.

There are terms in the sequence divisible by 2^n no matter how large n is.

(End)

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..63

FORMULA

a(n) = A140635(2*a(n-1)) - J. Lowell, May 20 2008

EXAMPLE

After a(3)=4 we argue as follows: 2*4 = 8 has 4 factors (1,2,4,8), but smallest number with 4 factors is 6, so a(4)=6.

CROSSREFS

Cf. A020697.

Cf. A140635.

Sequence in context: A095848 A208767 A136339 * A135614 A115387 A095849

Adjacent sequences:  A019502 A019503 A019504 * A019506 A019507 A019508

KEYWORD

nonn

AUTHOR

J. Lowell

STATUS

approved

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Last modified February 23 02:29 EST 2019. Contains 320411 sequences. (Running on oeis4.)