%I #14 Nov 04 2023 08:00:07

%S 8991,9375,335583,364256,488672,535328,677727,690848,755487,768608,

%T 864351,908576,924128,955232,1097631,1377567,1424223,1608416,1688607,

%U 1875231,2121632,2124063,2168288,2277152,2541536,2575071,2621727,2901663,3190624,3241376,3409375

%N Numbers n such that n and n + 1 are both of the form p*q^5 where p and q are distinct primes.

%C The smaller of adjacent values in A178740. - _R. J. Mathar_, Aug 08 2012

%H Chai Wah Wu, <a href="/A215198/b215198.txt">Table of n, a(n) for n = 1..10000</a>

%e 8991 is a member as 8991 = 37*3^5 and 8992 = 281*2^5.

%p with(numtheory):for n from 3 to 10^7 do:x:=factorset(n):y:=factorset(n+1):n1:=nops(x):n2:=nops(y):if n1=2 and n2=2 then xx1:=x[1]*x[2]^5 : xx2:=x[2]*x[1]^5:yy1:=y[1]*y[2]^5: yy2:=y[2]*y[1]^5:if (xx1=n or xx2=n) and (yy1=n+1 or yy2=n+1) then printf("%a, ", n):else fi:fi:od:

%t lst={}; Do[f1=FactorInteger[n]; If[Sort[Transpose[f1][[2]]]=={1, 5}, f2=FactorInteger[n+1]; If[Sort[Transpose[f2][[2]]]=={1, 5}, AppendTo[lst, n]]], {n, 3, 10^7}]; lst

%t SequencePosition[Table[If[Sort[FactorInteger[n][[;;,2]]]=={1,5},1,0],{n,341*10^4}],{1,1}][[;;,1]] (* _Harvey P. Dale_, Nov 04 2023 *)

%Y Cf. A074172, A178740, A215173, A215197.

%K nonn

%O 1,1

%A _Michel Lagneau_, Aug 05 2012