A215198 Numbers n such that n and n + 1 are both of the form p*q^5 where p and q are distinct primes.

8991, 9375, 335583, 364256, 488672, 535328, 677727, 690848, 755487, 768608, 864351, 908576, 924128, 955232, 1097631, 1377567, 1424223, 1608416, 1688607, 1875231, 2121632, 2124063, 2168288, 2277152, 2541536, 2575071, 2621727, 2901663, 3190624, 3241376, 3409375

Offset: 1

Author

Michel Lagneau, Aug 05 2012

Keywords

• nonn

Comments

The smaller of adjacent values in A178740. - R. J. Mathar, Aug 08 2012

Examples

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A074172, A178740, A215173, A215197.

Programs

Maple

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:

Mathematica

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