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

1,1

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A370372 A375760 A145989 * A352503 A071187 A329614

Adjacent sequences: A117180 A117181 A117182 * A117184 A117185 A117186

Keyword

nonn

Author

Leroy Quet, Mar 01 2006

Extensions

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

Status

approved