A304817 Number of divisors of n that are either 1 or not a perfect power.

1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 5, 2, 4, 4, 2, 2, 5, 2, 5, 4, 4, 2, 6, 2, 4, 2, 5, 2, 8, 2, 2, 4, 4, 4, 6, 2, 4, 4, 6, 2, 8, 2, 5, 5, 4, 2, 7, 2, 5, 4, 5, 2, 6, 4, 6, 4, 4, 2, 11, 2, 4, 5, 2, 4, 8, 2, 5, 4, 8, 2, 8, 2, 4, 5, 5, 4, 8, 2, 7, 2, 4, 2, 11, 4, 4

Offset: 1

Author

Gus Wiseman, May 18 2018

Keywords

• nonn

Comments

First differs from A183095 at a(80) = 8, A183095(80) = 7.

Examples

			The a(72) = 8 divisors of 72 that are either 1 or not a perfect power are {1, 2, 3, 6, 12, 18, 24, 72}. Missing are {4, 8, 9, 36}.
		

Crossrefs

Cf. A000005, A001597, A007916, A091050, A183096, A304326, A304362, A304653, A304779, A304819, A304820.

Programs

Mathematica

Table[DivisorSum[n,Boole[GCD@@FactorInteger[#][[All,2]]==1]&],{n,100}]

PARI

a(n) = sumdiv(n, d, !ispower(d)); \\ Michel Marcus, May 19 2018

Formula

a(n) = A183096(n) + 1.