A122144 -id:A122144 - cp's OEIS frontend

A122145 Numbers k such that q(k) < M(k) where q(k) is the largest prime divisor of k and M(k) is the largest prime power divisor of k.

4, 8, 9, 12, 16, 18, 24, 25, 27, 32, 36, 40, 45, 48, 49, 50, 54, 56, 63, 64, 72, 75, 80, 81, 90, 96, 98, 100, 108, 112, 120, 121, 125, 126, 128, 135, 144, 147, 150, 160, 162, 168, 169, 175, 176, 180, 189, 192, 196, 200, 208, 216, 224, 225, 240, 242, 243, 245, 250

Offset: 1

Douglas Stones (dssto1(AT)student.monash.edu.au), Aug 22 2006

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A006530, A034699, A122144, A122146.

Select[Range[250], Max[Power @@@ (f = FactorInteger[#])] > f[[-1, 1]] &] (* Amiram Eldar, May 23 2024 *)

is(n)=my(f=factor(n),k=#f[,1]);for(i=1,k, if(f[i,1]^f[i,2]>f[k,1], return(1)));0 \\ Charles R Greathouse IV, Sep 20 2012

Extended by Ray Chandler, Aug 23 2006

A122146 Numbers k such that q(k) = M(k) and 4*q(k) <= k, where q(k) is the largest prime divisor of k and M(k) is the largest prime power divisor of k.

Original entry on oeis.org

20, 28, 30, 35, 42, 44, 52, 55, 60, 65, 66, 68, 70, 76, 77, 78, 84, 85, 88, 91, 92, 95, 99, 102, 104, 105, 110, 114, 115, 116, 117, 119, 124, 130, 132, 133, 136, 138, 140, 143, 145, 148, 152, 153, 154, 155, 156, 161, 164, 165, 170, 171, 172, 174, 182, 184, 185

Offset: 1

Douglas Stones (dssto1(AT)student.monash.edu.au), Aug 22 2006

nonn

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

Cf. A006530, A034699, A122144, A122145.

Select[Range[200], Max[Power @@@ (f = FactorInteger[#])] == f[[-1, 1]] <= #/4 &] (* Amiram Eldar, May 23 2024 *)

isok(k) = {my(f = factor(k), pm = 0); if(k > 1 && 4 * f[#f~, 1] <= k, for(i = 1, #f~, pm = max(pm, f[i, 1]^f[i, 2])); pm == f[#f~, 1], 0);} \\ Amiram Eldar, May 23 2024

Edited by Ray Chandler, Aug 23 2006

A139703 Nonsquarefree positive integers k such that the largest prime power dividing k is prime.

Original entry on oeis.org

20, 28, 44, 52, 60, 68, 76, 84, 88, 92, 99, 104, 116, 117, 124, 132, 136, 140, 148, 152, 153, 156, 164, 171, 172, 184, 188, 198, 204, 207, 212, 220, 228, 232, 234, 236, 244, 248, 260, 261, 264, 268, 272, 276, 279, 284, 292, 296, 304, 306, 308, 312, 316, 328

Offset: 1

Leroy Quet, Jun 13 2008

nonn

			99 = 3^2 * 11^1. 99 is therefore not squarefree, because it is divisible by 3^2. Also, the largest prime power dividing 99 is 11^1. This is a prime, so 99 is included in the sequence.

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

Intersection of A013929 and A122144.

filter:= proc(n) local F,t,k;
  F:= ifactors(n)[2];
  if max(seq(t[2],t=F)) = 1 then return false fi;
  k:= max[index]([seq(t[1]^t[2],t=F)]);
  F[k,2]=1
end proc:
select(filter, [$2..1000]); # Robert Israel, Jan 31 2021

Select[Range[330], Max[(f = FactorInteger[#])[[;;, 2]]] > 1 && Max[Power @@@ f] == f[[-1, 1]] &] (* Amiram Eldar, Jun 26 2025 *)

This sequence consists of the nonsquarefree terms of A122144.

Extended by Ray Chandler, Jul 01 2009

cp's OEIS Frontend

A122145 Numbers k such that q(k) < M(k) where q(k) is the largest prime divisor of k and M(k) is the largest prime power divisor of k.

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A122146 Numbers k such that q(k) = M(k) and 4*q(k) <= k, where q(k) is the largest prime divisor of k and M(k) is the largest prime power divisor of k.

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A139703 Nonsquarefree positive integers k such that the largest prime power dividing k is prime.

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