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a(n) is the least start of exactly n consecutive numbers k that are sqrt(k)-smooth (A048098), or -1 if no such run exists.
1

%I #8 Jul 02 2022 14:37:49

%S 1,8,48,1518,5828,28032,304260,290783,1255500,4325170,11135837,

%T 18567909,321903029,1394350275,287946949,1659945758,38882519234

%N a(n) is the least start of exactly n consecutive numbers k that are sqrt(k)-smooth (A048098), or -1 if no such run exists.

%e a(2) = 8 since 8 and 9 are in A048098, 7 and 10 are not, and 8 is the least number with this property.

%t smQ[n_] := FactorInteger[n][[-1, 1]]^2 <= n; seq[len_, nmax_] := Module[{s = Table[0, {len}], v = {1}, n = 2, c = 0, m}, While[c <= len && n <= nmax, If[smQ[n], v = Join[v, {n}], m = Length[v]; v = {}; If[0 <= m <= len && s[[m]] == 0, c++; s[[m]] = n - m]]; n++]; s]; seq[6, 10^5]

%Y Cf. A048098, A355433.

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Jul 02 2022