A333004 a(n) is the smallest squarefree number k such that sum of reciprocals of squarefree numbers up to k (squarefree harmonic sum) exceeds n.

1, 2, 5, 26, 130, 670, 3466, 17985, 93179, 482762, 2501013, 12956855, 67125243, 347753857, 1801596939

Offset: 0

Author

Ilya Gutkovskiy, Mar 05 2020

Keywords

• nonn
• hard
• more

Comments

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

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Squarefree

Crossrefs

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

Cf. A005117 (squarefree numbers).

Extensions

a(11)-a(14) from Daniel Suteu, Mar 05 2020