A156237 Smallest hexagonal number with n distinct prime factors.

6, 66, 630, 7140, 103740, 1272810, 56812470, 1722580860, 48098217090, 1850186768430, 139261952960130, 17743036637876550, 741902728913225880, 21549201398378163510, 2378522762792139793830, 351206814022419685159830

Offset: 2

Author

Donovan Johnson, Feb 07 2009

Keywords

• nonn

Comments

a(18) <= 45781615623002935783197090. - Donovan Johnson, Feb 15 2012

Examples

			a(9) = 1722580860 = 2^2*3*5*7*11*13*23*29*43. 1722580860 is the smallest hexagonal number with 9 distinct prime factors.
		

Links

• Eric Weisstein's World of Mathematics, Hexagonal Numbers.

Crossrefs

Cf. A000384, A076551, A156236, A156238, A156239.

Programs

Mathematica

Module[{nn=167*10^5,c},c={#,PrimeNu[#]}&/@PolygonalNumber[6,Range[nn]];Table[ SelectFirst[ c,#[[2]]==n&],{n,2,12}]][[;;,1]] (* The program generates the first 11 terms of the sequence. *) (* Harvey P. Dale, Jan 19 2024 *)