A332991 a(n) is the smallest prime power p^k (p prime, k >= 1) such that sum of reciprocals of prime powers up to p^k (prime power harmonic sum) exceeds n.

2, 4, 19, 1307, 266655247

Offset: 0

Author

Ilya Gutkovskiy, Mar 05 2020

Keywords

• nonn
• hard
• more

Comments

The corresponding indices of a(n) in A246655 are 1, 3, 12, 240, ...

Examples

			a(1) = 4 because 1/2 + 1/3 = 0.8333... < 1 but 1/2 + 1/3 + 1/4 = 1.0833... > 1.
		

Links

• Eric Weisstein's World of Mathematics, Prime Power

Crossrefs

Similar sequences: A002387 (for positive integers), A016088 (for primes), A076751 (for composite numbers), A333004 (for squarefree numbers).

Cf. A246655 (prime powers).

Extensions

a(4) from Daniel Suteu, Mar 05 2020