A071147 Smallest squarefree number k with exactly n prime factors such that the sum of the prime factors is divisible by the largest prime dividing k, or 0 if no such k exists.

1, 2, 0, 30, 3135, 3570, 72930, 1231230, 14804790, 497668710, 14908423530, 278196808890, 12192694624110, 550939666387110, 21275256232500270, 1458502323630662310, 87988283090327810190, 3254611619240885033130, 261462818462495728868790, 9965666894849284108299810, 557940830126698960967415390, 90544636506979071680577724410

Offset: 0

Author

Labos Elemer, May 13 2002

Keywords

• nonn

Comments

No solution exists for n=2, so a(2)=0.

Examples

			a(0) =       1 = 1;
a(1) =       2 = 2;
a(3) =      30 = 2 *  3 *  5;
a(4) =    3135 = 3 *  5 * 11 * 19;
a(5) =    3570 = 2 *  3 *  5 *  7 * 17;
a(6) =   72930 = 2 *  3 *  5 * 11 * 13 * 17;
a(7) = 1231230 = 2 *  3 *  5 *  7 * 11 * 13 * 41.
		

Crossrefs

Cf. A008472, A006530, A000961, A025475, A037074, A071139-A071146.

Formula

A008472(k)/A006530(k) is an integer; k is squarefree and has exactly n prime factors.

Extensions

Corrected and extended by Donovan Johnson, Apr 22 2008

Name corrected by Jon E. Schoenfield, Jul 08 2018