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A072697
Squarefree numbers such that the sum of the prime factors is a multiple of the number of prime factors.
6
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
1,1
LINKS
EXAMPLE
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.
MATHEMATICA
Select[ Range[2, 143], SquareFreeQ[#] && Divisible[ Tr[ fi = FactorInteger[#][[All, 1]]], Length[fi]]& ](* Jean-François Alcover, Jul 11 2012 *)
PROG
(Magma) [k:k in [2..200]| IsSquarefree(k) and IsIntegral(&+PrimeDivisors(k)/#PrimeDivisors(k))]; // Marius A. Burtea, Nov 14 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 04 2002
STATUS
approved