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

1,2

Comments

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

Links

Table of n, a(n) for n=1..86.

Formula

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

Example

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}.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A073180 A316398 A183095 * A242802 A277561 A317684

Adjacent sequences: A304814 A304815 A304816 * A304818 A304819 A304820

Keyword

nonn

Author

Gus Wiseman, May 18 2018

Status

approved