OFFSET
1,1
COMMENTS
Each term is the first of a consecutive pair of nonsquarefree integers whose cores are consecutive too.
If c and c+1 are squarefree, then the sequence contains all the numbers c*x^2 where x is a solution to the Diophantine equation c*x^2+1 = (c+1)*y^2, with x,y > 1, hence the sequence is infinite.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..1328 (terms < 10^12)
EXAMPLE
182182 is a term, because 182182 = 2*7^2*11*13^2 and 182183 = 23*89^2, so core(182182) = 22 and core(182183) = 23.
MATHEMATICA
core[n_] := Times@@ ((#[[1]] ^ Mod[#[[2]], 2]) & /@ FactorInteger@n); Select[ Range[10^5], # != core[#] == core[#+1]-1 &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Giovanni Resta, Jul 19 2015
STATUS
approved