A120055 a(n) is the least semiprime s such that the Sum_{semiprime i <= s} 1/i exceeds n.

4, 35, 871, 43217, 5296623, 2011783478

Offset: 0

Author

Jonathan Vos Post and Robert G. Wilson v, Mar 25 2006

Keywords

• nonn
• more

Comments

A002387(n+1) < a(n) < A016088(n).

a(n) is the k-th semiprime: k = 1, 13, 262, 10521, 1034924, 316108902; factors: 2*2, 5*7, 13*61, 23*1879, 3*1765541, 2*1005891739.

For a(1), sum = 1.025694370988488635...

for a(2), sum = 2.000920208207319042...

for a(3), sum = 3.000000294546501318...

for a(4), sum = 4.000000031685702432...

for a(5), sum = 5.000000000169814007...

Examples

			a(0)=4 because 1/4 > 0.
a(1)=35 because 1/4 + 1/6 + 1/9 + 1/10 + 1/14 + 1/15 + 1/21 + 1/22 + 1/25 + 1/26 + 1/33 + 1/34 + 1/35 = 15708817/15315300 > 1.
		

Crossrefs

Cf. A002387, A016088.

Programs

Mathematica

s = 0; k = 1; Do[ While[s <= n, If[ Plus @@ Last /@ FactorInteger@k == 2, s = N[ s + 1/k, 20]]; k++ ]; Print[{k - 1, s}]; k ++, {n, 0, 5}]