A074174 Smallest number k such that k and k+n are of the form p^2*q where p and q are primes.

44, 18, 172, 171, 45, 12, 45, 12, 236, 18, 52, 63, 50, 261, 524, 12, 28, 45, 44, 637, 404, 28, 45, 20, 20, 18, 18, 147, 63, 20, 44, 12, 12, 18, 28, 63, 116, 12, 236, 12, 75, 50, 20, 325, 18, 52, 28, 20, 50, 18, 12, 423, 45, 44, 20, 12, 18, 18, 116, 147, 63, 325, 12, 12, 52

Offset: 1

Author

Amarnath Murthy, Aug 30 2002

Keywords

• nonn

Examples

			a(2) = 18 as 18 = 3^2*2 and 18 +2 =20 = 2^2*5.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A074172, A074173, A054753.

Programs

Mathematica

Table[k=1; found=False; While[ !found, k++; f1=FactorInteger[k]; If[Sort[Transpose[f1][[2]]]=={1, 2}, f2=FactorInteger[k+n]; If[Sort[Transpose[f2][[2]]]=={1, 2}, found=True]]]; k, {n, 100}]
snk[n_]:=Module[{k=1},While[Sort[FactorInteger[k][[All,2]]]!={1,2} || Sort[FactorInteger[k+n][[All,2]]]!={1,2},k++];k]; Array[snk,70]

Extensions

Corrected and extended by T. D. Noe, Oct 04 2004