A085683 a(n) = Sum_{k = 1..N-1} floor(N/k) where N is the n-th prime.

2, 4, 9, 15, 28, 36, 51, 59, 75, 102, 112, 141, 159, 169, 187, 218, 248, 262, 293, 313, 327, 357, 378, 412, 460, 483, 493, 515, 529, 553, 636, 658, 696, 706, 767, 781, 821, 857, 877, 918, 952, 972, 1032, 1048, 1071, 1085, 1167, 1239, 1266, 1280, 1306, 1342, 1364, 1422

Offset: 1

Author

N. J. A. Sloane, Oct 28 2008

Keywords

• nonn

Comments

The old entry with this sequence number was a duplicate of A081532.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• R. K. Guy, Conway's prime producing machine, Math. Mag. 56 (1983), no. 1, 26-33 (see p. 33).

Crossrefs

Cf. A006218, A077597.

Programs

Mathematica

(Rest@ FoldList[ Plus, 0, DivisorSigma[0, Range@ Prime@ 100]])[[ Prime@ Range@ 100]] -1 (* Giovanni Resta, Jun 09 2015 *)

Python

from math import isqrt
from sympy import prime
def A085683(n): return -(s:=isqrt(m:=prime(n)))**2+(sum(m//k for k in range(1,s+1))<<1)-1 # Chai Wah Wu, Oct 23 2023