A143176 a(1)=1. a(n) is the smallest positive multiple of n that has more divisors than a(n-1) has.

1, 2, 6, 12, 30, 36, 84, 120, 180, 240, 660, 720, 1560, 1260, 1680, 2880, 6120, 5040, 15960, 10080, 15120, 27720, 115920, 83160, 138600, 196560, 302400, 277200, 803880, 498960, 1562400, 665280, 720720, 1413720, 1441440, 2162160, 8205120

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..89 (terms 1..60 from Michael De Vlieger)

Example

a(4)=12 has 6 divisors. Checking the multiples of 5: 1*5=5 has 2 divisors. 2*5=10 has 4 divisors. 3*5=15 has 4 divisors. 4*5=20 has 6 divisors. 5*5=25 has 3 divisors. So the first 5 positive multiples of 5 each have <= 6 divisors. But 6*5 = 30 has 8 divisors. And since 8 > 6, a(5) = 30.

Mathematica

FoldList[Block[{d = DivisorSigma[0, #1], k = 1, m}, While[DivisorSigma[0, Set[m, k #2]] <= d, k++]; m] &, Range@ 37] (* Michael De Vlieger, Aug 29 2017 *)

Crossrefs

Cf. A143177, A143178.

Sequence in context: A358070 A237704 A181826 * A081375 A024701 A224532

Adjacent sequences: A143173 A143174 A143175 * A143177 A143178 A143179

Keyword

nonn

Author

Leroy Quet, Jul 28 2008

Extensions

a(9)-a(37) from Donovan Johnson, Sep 05 2008

Status

approved