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a(n) is the denominator of the sum of the reciprocals of the first n squarefree numbers.
2

%I #7 May 26 2022 09:52:51

%S 1,2,6,30,5,35,70,770,10010,5005,15015,255255,4849845,1616615,3233230,

%T 74364290,37182145,1078282205,6469693230,200560490130,6077590610,

%U 3038795305,607759061,22487085257,44974170514,134922511542,5531822973222,921970495537,39644731308091

%N a(n) is the denominator of the sum of the reciprocals of the first n squarefree numbers.

%e 1, 3/2, 11/6, 61/30, 11/5, 82/35, 171/70, 1951/770, 26133/10010, 13424/5005, 41273/15015, ...

%t Accumulate[1/Select[Range[43], SquareFreeQ]] // Denominator

%o (PARI) a(n) = my(i=0, s=0); for(x=1, oo, if(core(x)==x, s+=1/x; i++; if(i==n, return(denominator(s))))) \\ _Felix Fröhlich_, May 26 2022

%Y Cf. A002110, A002805, A005117, A034386, A051451, A072983, A354417 (numerators).

%K nonn,frac

%O 1,2

%A _Ilya Gutkovskiy_, May 26 2022