A072698 -id:A072698 - cp's OEIS frontend

A072700 A072698(n) / A072699(n).

2, 3, 5, 7, 11, 13, 4, 17, 19, 5, 23, 29, 31, 7, 6, 37, 8, 41, 4, 43, 47, 10, 53, 8, 11, 59, 61, 9, 67, 13, 71, 73, 9, 6, 79, 83, 11, 16, 89, 10, 17, 12, 97, 101, 103, 5, 107, 109, 6, 20, 113, 8, 14, 12, 22, 127, 23, 131, 13, 137, 139, 25, 12, 17, 149, 151, 18, 157, 28, 15

Offset: 1

Reinhard Zumkeller, Jul 04 2002

nonn

			a(19) = A072698(19)/A072699(19) = 12/3 = 4.

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

Cf. A005117, A072701, A072697.

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

Original entry on oeis.org

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

Reinhard Zumkeller, Jul 04 2002

nonn

			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.

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

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

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

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

A072699 Number of prime factors of A072697(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 3, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 3, 1, 1, 3, 2, 1, 3, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 3, 2, 1, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 3, 1, 1, 1, 3, 3, 1, 2, 2

Offset: 1

Reinhard Zumkeller, Jul 04 2002

nonn

a(n) = A001222(A072697(n)) = A001221(A072697(n)).

			a(19) = A001222(A072697(19)) = A001222(42) = A001222(2*3*7) = 3.

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

Cf. A072698, A072700.

cp's OEIS Frontend

A072700 A072698(n) / A072699(n).

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

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A072699 Number of prime factors of A072697(n).

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