A117183 a(n) = smallest prime dividing n-th nonsquarefree positive integer.

2, 2, 3, 2, 2, 2, 2, 2, 5, 3, 2, 2, 2, 2, 2, 3, 2, 7, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 11, 2, 5, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 13, 3, 2, 5, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 5, 2, 2, 2, 2, 2, 3, 2, 2, 2

Offset: 1

Author

Leroy Quet, Mar 01 2006

Keywords

• nonn

Examples

			12, the 4th nonsquarefree positive integer, is 2^2 * 3. 2 is the smallest prime dividing 12. So a(4) = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A013929, A020639, A073481, A115074, A115090.

Programs

Maple

with(numtheory): a:=proc(n) if mobius(n)=0 then op(1,factorset(n)) fi end: seq(a(n),n=1..345); # Emeric Deutsch

Mathematica

FactorInteger[ # ][[1, 1]] & /@ Select[ Range@252, !SquareFreeQ@# &] (* Robert G. Wilson v, Mar 06 2006 *)
FactorInteger[#][[1,1]]&/@DeleteCases[Range[300],?SquareFreeQ] (* _Harvey P. Dale, Jun 02 2017 *)

PARI

list(lim) = apply(x -> factor(x)[1,1], select(x -> !issquarefree(x), vector(lim, i, i))); \\ Amiram Eldar, Jun 25 2025

Formula

a(n) = A020639(A013929(n)).

Extensions

More terms from Emeric Deutsch and Robert G. Wilson v, Mar 06 2006