A072697 Squarefree numbers such that the sum of the prime factors is a multiple of the number of prime factors.

2, 3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 29, 31, 33, 35, 37, 39, 41, 42, 43, 47, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 77, 78, 79, 83, 85, 87, 89, 91, 93, 95, 97, 101, 103, 105, 107, 109, 110, 111, 113, 114, 115, 119, 123, 127, 129, 131, 133, 137, 139, 141, 143

Offset: 1

Author

Reinhard Zumkeller, Jul 04 2002

Keywords

• nonn

Examples

			42=2*3*7: number of factors = 3 and sum of factors =2+3+7=12, as 12=4*3, 42 is a term: a(19)=42, A072698(19)=3, A072699(19)=12 and A072700(19)=4 contributes 1 count for A072701(4), as (2+3+7)/3=4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A072700, A072701, A072698, A072699.

Programs

Magma

[k:k in [2..200]| IsSquarefree(k) and IsIntegral(&+PrimeDivisors(k)/#PrimeDivisors(k))]; // Marius A. Burtea, Nov 14 2019

Mathematica

Select[ Range[2, 143], SquareFreeQ[#] && Divisible[ Tr[ fi = FactorInteger[#][[All, 1]]], Length[fi]]& ](* Jean-François Alcover, Jul 11 2012 *)