A143178 a(1)=1. a(n) is the smallest positive multiple of n that has more, or the same number of, divisors than a(n-1) has.

1, 2, 3, 4, 10, 6, 14, 8, 18, 20, 44, 12, 52, 28, 30, 48, 204, 72, 228, 60, 84, 132, 276, 72, 150, 156, 108, 84, 348, 60, 372, 96, 132, 204, 140, 72, 444, 228, 156, 120, 984, 168, 1032, 264, 180, 828, 1692, 240, 1176, 600, 1020, 780, 3180, 540, 660, 504, 1140, 1740

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..500

Example

a(10) = 20, which has 6 divisors. Checking, for n = 11: 1*11=11 has 2 divisors. 2*11=22 has 4 divisors. 3*11=33 has 4 divisors. Each of these positive multiples of 11 has < 6 divisors. But 4*11=44 has 6 divisors. And since 6 >=6, then a(11) = 44.

Mathematica

nxt[{n_, a_}]:=Module[{k=1}, While[DivisorSigma[0, a]>DivisorSigma[ 0, k(n+1)], k++]; {n+1, k(n+1)}]; Transpose[NestList[nxt, {1, 1}, 60]][[2]] (* Harvey P. Dale, Sep 22 2014 *)

Crossrefs

Cf. A143176, A143179.

Sequence in context: A111619 A241083 A334463 * A084190 A377484 A203070

Adjacent sequences: A143175 A143176 A143177 * A143179 A143180 A143181

Keyword

nonn

Author

Leroy Quet, Jul 28 2008

Extensions

a(13)-a(58) from Donovan Johnson, Sep 05 2008

Status

approved