A156899 -id:A156899 - cp's OEIS frontend

A081217 Greatest squarefree number not exceeding n-th prime power.

1, 2, 3, 3, 5, 7, 7, 7, 11, 13, 15, 17, 19, 23, 23, 26, 29, 31, 31, 37, 41, 43, 47, 47, 53, 59, 61, 62, 67, 71, 73, 79, 79, 83, 89, 97, 101, 103, 107, 109, 113, 119, 123, 127, 127, 131, 137, 139, 149, 151, 157, 163, 167, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223

Offset: 1

Reinhard Zumkeller, Mar 10 2003

nonn

a(n) = A070321(A000961(n)).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A081218.

Cf. A156898, A156899, A156900, A005117, A000961

n:= 0:
for m from 1 while n <= 100 do
  if numtheory:-issqrfree(m) then s:= m fi;
  if nops(numtheory:-factorset(m)) <= 1 then n:= n+1; A[n]:= s fi
od:
seq(A[i],i=1..100); # Robert Israel, Jan 08 2018

nmax = 100; coeff = 5;
A000961 = Join[{1}, Select[Range[2, coeff*nmax],PrimePowerQ]];
a070321[n_] := For[k = n, True, k--, If[SquareFreeQ[k], Return[k]]];
a[n_] := If[n > Length[A000961], Print["error: increase insufficient coeff ", coeff], a070321[A000961[[n]] ] ];
Array[a, nmax] (* Jean-François Alcover, Mar 08 2019 *)

A156898 a(n) = the smallest squarefree integer >= the n-th prime power.

Original entry on oeis.org

1, 2, 3, 5, 5, 7, 10, 10, 11, 13, 17, 17, 19, 23, 26, 29, 29, 31, 33, 37, 41, 43, 47, 51, 53, 59, 61, 65, 67, 71, 73, 79, 82, 83, 89, 97, 101, 103, 107, 109, 113, 122, 127, 127, 129, 131, 137, 139, 149, 151, 157, 163, 167, 170, 173, 179, 181, 191, 193, 197, 199, 211

Offset: 1

Leroy Quet, Feb 17 2009, Feb 18 2009

nonn

The first prime power is considered to be 1 here.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A081217, A156899, A156900, A005117, A000961.

Block[{nn = 216, s}, s = {1}~Join~Select[Range[nn], PrimePowerQ]; Map[SelectFirst[# + Range[0, #], SquareFreeQ] &, s]] (* Michael De Vlieger, Oct 30 2017 *)

Extended by Ray Chandler, Jun 19 2009

A156900 a(n) = the smallest prime power >= the n-th positive squarefree integer.

Original entry on oeis.org

1, 2, 3, 5, 7, 7, 11, 11, 13, 16, 16, 17, 19, 23, 23, 23, 27, 29, 31, 31, 37, 37, 37, 37, 41, 41, 41, 43, 43, 47, 47, 53, 53, 59, 59, 59, 59, 61, 64, 67, 67, 67, 71, 71, 71, 73, 79, 79, 79, 79, 83, 83, 89, 89, 89, 89, 97, 97, 97, 97, 97, 101, 103, 103, 107, 107, 107, 109, 113

Offset: 1

Leroy Quet, Feb 17 2009

nonn

The first positive squarefree integer is considered to be 1 here.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A081217, A156898, A156899, A005117, A000961.

Block[{nn = 110, s}, s = Select[Range[nn], SquareFreeQ]; Map[If[# == 1, 1, SelectFirst[# + Range[0, # - 1], PrimePowerQ]] &, s]] (* Michael De Vlieger, Oct 30 2017 *)

Extended by D. S. McNeil, Mar 23 2009

cp's OEIS Frontend

A081217 Greatest squarefree number not exceeding n-th prime power.

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A156898 a(n) = the smallest squarefree integer >= the n-th prime power.

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Mathematica

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A156900 a(n) = the smallest prime power >= the n-th positive squarefree integer.

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Author

Keywords

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Crossrefs

Programs

Mathematica

Extensions