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

0,1

Comments

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

Links

Table of n, a(n) for n=0..4.

Eric Weisstein's World of Mathematics, Prime Power

Example

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

Crossrefs

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

Cf. A246655 (prime powers).

Sequence in context: A048774 A061213 A063458 * A132530 A316389 A133521

Adjacent sequences: A332988 A332989 A332990 * A332992 A332993 A332994

Keyword

nonn,hard,more

Author

Ilya Gutkovskiy, Mar 05 2020

Extensions

a(4) from Daniel Suteu, Mar 05 2020

Status

approved