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a(n) is the smallest squarefree number k such that sum of reciprocals of squarefree numbers up to k (squarefree harmonic sum) exceeds n.
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%I #8 Mar 05 2020 22:55:33

%S 1,2,5,26,130,670,3466,17985,93179,482762,2501013,12956855,67125243,

%T 347753857,1801596939

%N a(n) is the smallest squarefree number k such that sum of reciprocals of squarefree numbers up to k (squarefree harmonic sum) exceeds n.

%C The corresponding indices of a(n) in A005117 are 1, 2, 4, 17, 80, 409, 2112, 10936, 56651, 293483, 1520429, ...

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>

%e a(2) = 5 because 1/1 + 1/2 + 1/3 = 1.8333... < 2 but 1/1 + 1/2 + 1/3 + 1/5 = 2.0333... > 2.

%Y Similar sequences: A002387 (for positive integers), A016088 (for primes), A076751 (for composite numbers), A332991 (for prime powers).

%Y Cf. A005117 (squarefree numbers).

%K nonn,hard,more

%O 0,2

%A _Ilya Gutkovskiy_, Mar 05 2020

%E a(11)-a(14) from _Daniel Suteu_, Mar 05 2020