A108274 Sum of the first 10^n terms in A097974. a(n) = sum_{m=1..10^n} t(m), where t(m) is the sum of the prime divisors of m that are less than or equal to sqrt(m).

0, 11, 327, 7714, 184680, 4617253, 118697919, 3149768778, 85356405077, 2357169671137, 66097467843823, 1875931900135854, 53804720498131760, 1556256544987695973, 45343922927650954928, 1329347125287604758708, 39180941384720954859005

Offset: 0

Author

Ryan Propper, Jul 24 2005

Keywords

• nonn

Comments

Does a(n+1)/a(n) converge?

Examples

			The first 10^2 terms in A097974 sum to 327, so a(2) = 327.
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 0..19

Crossrefs

Cf. A097974.

Programs

Mathematica

s = 0; k = 1; Do[s += Plus @@ Select[Select[Divisors[n], PrimeQ], #<=Sqrt[n] &]; If[n == k, Print[s]; s = 0; k *= 10], {n, 1, 10^7}]

PARI

a(n) = sum(m=1, 10^n, sumdiv(m, d, d*isprime(d)*(d<=sqrt(m)))); \\ Michel Marcus, Jul 07 2014

Extensions

a(2)-a(7) and the example corrected and a(8)-a(16) from Hiroaki Yamanouchi, Jul 07 2014