A115090 -id:A115090 - cp's OEIS frontend

A115074 a(n) is the largest prime dividing the n-th nonsquarefree positive integer.

2, 2, 3, 3, 2, 3, 5, 3, 5, 3, 7, 2, 3, 5, 11, 5, 3, 7, 5, 13, 3, 7, 5, 7, 2, 17, 3, 5, 19, 5, 3, 7, 11, 5, 23, 3, 7, 11, 5, 13, 3, 7, 29, 13, 5, 11, 31, 5, 7, 2, 11, 5, 17, 7, 3, 7, 37, 5, 19, 17, 13, 5, 3, 41, 7, 13, 19, 43, 7, 11, 5, 23, 47, 7, 3, 7, 11, 5, 17, 23, 13, 53, 3, 11, 7, 5, 19, 29, 13

Offset: 1

Leroy Quet, Mar 01 2006

nonn

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A117183, A115090, A013929, A006530.

with(numtheory): a:=proc(n) if mobius(n)=0 then op(nops(factorset(n)),factorset(n)) fi end: seq(a(n),n=1..270); # Emeric Deutsch, Mar 06 2006

FactorInteger[ # ][[ -1, 1]] & /@ Select[ Range@235, !SquareFreeQ@# &] (* Robert G. Wilson v, Mar 09 2006 *)

a(n) = A006530(A013929(n)).

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

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

Original entry on oeis.org

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

Leroy Quet, Mar 01 2006

nonn

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

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

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

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

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 *)

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

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

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

cp's OEIS Frontend

A115074 a(n) is the largest prime dividing the n-th nonsquarefree positive integer.

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