A074174 - OEIS

%I #9 Jun 02 2020 18:17:13

%S 44,18,172,171,45,12,45,12,236,18,52,63,50,261,524,12,28,45,44,637,

%T 404,28,45,20,20,18,18,147,63,20,44,12,12,18,28,63,116,12,236,12,75,

%U 50,20,325,18,52,28,20,50,18,12,423,45,44,20,12,18,18,116,147,63,325,12,12,52

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

%H Harvey P. Dale, <a href="/A074174/b074174.txt">Table of n, a(n) for n = 1..1000</a>

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

%t 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}]

%t 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]

%Y Cf. A074172, A074173, A054753.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Aug 30 2002

%E Corrected and extended by _T. D. Noe_, Oct 04 2004