A086534 - OEIS

%I #8 Dec 05 2013 19:56:19

%S 2,17,271,1249,13121,13121,153089,1272833,28146689,193562623,

%T 652963841,1378557953,29096394751,316431663103,2191221587969,

%U 15356401156097,128200797454337,314394051346433,314394051346433,28344942091829249,201993039632138239,267803891553271807

%N Smallest prime p sandwiched between two numbers that are divisible by n-th powers.

%C Conjecture: sequence is finite.

%e a(3) = 271, 270 = 3^3*10 and 272 = 2^3*34. 271 is the smallest such number.

%e a(4) = 1249, 1248 =2^4*78, 1250 = 5^4*2. 1250 is the smallest such number.

%t PrimeExponents[n_] := Max[ Flatten[ Table[ # [[2]], {1}] & /@ FactorInteger[n]]]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = Table[0, {15}]; p = 1; Do[p = NextPrim[p]; b = Min[ PrimeExponents[p - 1], PrimeExponents[p + 1]]; If[ a[[b]] == 0, a[[b]] = p; Print[b, " ", p]], {n, 1, 70000000}]; a

%Y Cf. A086708, A086709.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Aug 17 2003

%E Edited and extended by _Robert G. Wilson v_, Aug 18 2003

%E a(5) corrected. a(13)-a(22) from _Donovan Johnson_, Sep 02 2008