A108298 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).
0, 30, 1797, 132946, 10034416, 790688821, 64867780292, 5492352229154, 475943074590494, 41984058676639733, 3755707610763952011, 339758793864093720073, 31019273006095379281810, 2853680710328414627392965, 264227600111858563511104972
Offset: 0
Examples
The first 10^2 terms in A097975 sum to 1797, so a(2) = 1797.
Crossrefs
Cf. A097975.
Programs
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Mathematica
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}] -
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(14) from Hiroaki Yamanouchi, Jul 07 2014
Comments