A160813 a(n) = n-th squarefree number plus n-th cubefree number.

2, 4, 6, 9, 11, 13, 17, 20, 23, 25, 27, 30, 33, 36, 39, 41, 45, 49, 51, 53, 56, 59, 61, 65, 67, 69, 72, 75, 77, 81, 83, 88, 91, 94, 98, 100, 102, 105, 107, 111, 113, 116, 119, 121, 123, 126, 129, 134, 136, 138, 142, 144, 147, 149, 152, 155, 158, 161, 163, 165, 168

Offset: 1

Author

Jonathan Vos Post, Jan 19 2011

Keywords

• nonn
• easy

Examples

			a(1) = 1+1 = 2.
a(4) = 5+4 = 9.
a(8) = 11+9 = 20.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A004709, A005117, A046100, A347213.

Programs

Mathematica

Module[{nn=100,sf,cf,len},sf=Select[Range[nn],SquareFreeQ];cf=Select[ Range[ nn],Max[FactorInteger[#][[All,2]]]<3&];len=Min[ Length[ sf], Length[cf]];Total/@Thread[{Take[sf,len],Take[cf,len]}]] (* Harvey P. Dale, Oct 01 2019 *)

Formula

a(n) = A005117(n) + A004709(n).

a(n) ~ c*n, where c = zeta(2) + zeta(3) (A347213). - Amiram Eldar, Sep 24 2023