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

0,2

Comments

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

Links

Table of n, a(n) for n=0..21.

Formula

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

Example

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.

Sequence in context: A340534 A104466 A086487 * A156481 A176726 A156452

Adjacent sequences: A071144 A071145 A071146 * A071148 A071149 A071150

Keyword

nonn

Author

Labos Elemer, May 13 2002

Extensions

Corrected and extended by Donovan Johnson, Apr 22 2008

Name corrected by Jon E. Schoenfield, Jul 08 2018

Status

approved