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

1,1

Links

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

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

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

Sequence in context: A325162 A331635 A320055 * A102553 A069161 A328603

Adjacent sequences: A072694 A072695 A072696 * A072698 A072699 A072700

Keyword

nonn

Author

Reinhard Zumkeller, Jul 04 2002

Status

approved