A178032 Numbers n such that n, n+1, n+2 are all of the form p*q^2 for distinct primes p,q.

603, 2523, 4203, 4923, 7442, 10467, 18027, 20402, 54475, 58923, 79011, 97675, 104211, 118323, 120787, 122571, 124891, 132723, 134307, 148075, 200491, 229707, 243602, 246571, 249307, 258507, 303651, 324331, 331387, 370827, 385675

Offset: 1

Author

John L. Drost, Dec 16 2010

Keywords

• nonn

Examples

			603=3*3*67, 604=2*2*151, 605=5*11*11
2523=3*29*29, 2524=2*2*631, 2525=5*5*101
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000 (first 500 terms from Harvey P. Dale)
• Index to sequences related to prime signature

Crossrefs

Cf. A054753, A074172, A308683, A141621.

Programs

Mathematica

SequencePosition[Table[If[Sort[FactorInteger[n][[All,2]]]=={1,2},1,0],{n,400000}],{1,1,1}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 30 2019 *)

Sage

is_A178032 = lambda n: all(sorted(m for p,m in factor(k)) == [1, 2] for k in (n, n+1, n+2)) # D. S. McNeil, Dec 17 2010

Extensions

Corrected and extended by D. S. McNeil, Dec 16 2010