A308736 -id:A308736 - cp's OEIS frontend

A074173 Numbers n such that n and n+2 are of the form p^2*q where p and q are distinct primes.

18, 50, 242, 423, 475, 603, 637, 722, 845, 925, 1682, 1773, 2007, 2523, 2525, 2527, 3175, 3177, 4203, 4475, 4525, 4923, 5823, 6725, 6811, 6962, 7299, 7442, 7675, 8425, 8957, 8973, 9457, 9925, 10051, 10082, 10467, 11673, 11709, 12427, 12482, 12591

Offset: 1

Amarnath Murthy, Aug 30 2002

nonn

			18 is a member as 18 = 3^2*2 and 20 = 2^2*5.

Ray Chandler, Table of n, a(n) for n = 1..10000
Index to sequences related to prime signature

Cf. A048161, A054753, A074172, A074174, A308735, A308736.

lst={}; Do[f1=FactorInteger[n]; If[Sort[Transpose[f1][[2]]]=={1, 2}, f2=FactorInteger[n+2]; If[Sort[Transpose[f2][[2]]]=={1, 2}, AppendTo[lst, n]]], {n, 3, 10000}]; lst

Even terms in sequence are 2*A048161(n)^2. - Ray Chandler, Jun 24 2019

More terms from T. D. Noe, Oct 04 2004

A308735 Numbers k such that k, k+2, k+4 are of the form p^2*q where p and q are distinct primes.

Original entry on oeis.org

2523, 2525, 3175, 22021, 25529, 28223, 40325, 53573, 58923, 73447, 122571, 132021, 149675, 152339, 165175, 172917, 202221, 209673, 235825, 267773, 268223, 308671, 322223, 371075, 425723, 430171, 445923, 488975, 575973, 591575

Offset: 1

Ray Chandler, Jun 24 2019

nonn

All terms are odd. See comment in A308736. - Chai Wah Wu, Jun 24 2019

			3175 =  5 *  5 * 127,
3177 =  3 *  3 * 353,
3179 = 11 * 17 *  17.

Ray Chandler, Table of n, a(n) for n = 1..10000

Cf. A074173, A308736.

psx = Table[{0}, {5}]; nmax = 600000; n = 1; lst = {};
While[n < nmax, n++;
  psx = RotateRight[psx];
  psx[[1]] = Sort[Last /@ FactorInteger[n]];
  If[Union[{psx[[1]], psx[[3]], psx[[5]]}] == {{1, 2}},
   AppendTo[lst, n - 4]];];
lst

cp's OEIS Frontend

A074173 Numbers n such that n and n+2 are of the form p^2*q where p and q are distinct primes.

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