A108298 - OEIS

%I #8 Jul 07 2014 07:33:49

%S 0,30,1797,132946,10034416,790688821,64867780292,5492352229154,

%T 475943074590494,41984058676639733,3755707610763952011,

%U 339758793864093720073,31019273006095379281810,2853680710328414627392965,264227600111858563511104972

%N Sum of the first 10^n terms in A097975. a(n) = sum_{m=1..10^n} t(m), where t(m) is the sum of the prime divisors of m that are greater than or equal to sqrt(m).

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

%e The first 10^2 terms in A097975 sum to 1797, so a(2) = 1797.

%t s = 0; k = 1; Do[l = Select[Select[Divisors[n], PrimeQ], # >= Sqrt[n]&]; If[Length[l] > 0, s += l[[1]]]; If[n == k, Print[s]; s = 0; k *= 10], {n, 1, 10^7}]

%o (PARI) a(n) = sum(m=1, 10^n, sumdiv(m, d, d*isprime(d)*(d>=sqrt(m)))); \\ _Michel Marcus_, Jul 07 2014

%Y Cf. A097975.

%K more,nonn

%O 0,2

%A _Ryan Propper_, Jul 24 2005

%E a(2)-a(7) and the example corrected and a(8)-a(14) from _Hiroaki Yamanouchi_, Jul 07 2014