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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). 1

%I

%S 0,11,327,7714,184680,4617253,118697919,3149768778,85356405077,

%T 2357169671137,66097467843823,1875931900135854,53804720498131760,

%U 1556256544987695973,45343922927650954928,1329347125287604758708,39180941384720954859005

%N 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).

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

%H Hiroaki Yamanouchi, <a href="/A108274/b108274.txt">Table of n, a(n) for n = 0..19</a>

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

%t 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}]

%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. A097974.

%K nonn

%O 0,2

%A _Ryan Propper_, Jul 24 2005

%E a(2)-a(7) and the example corrected and a(8)-a(16) from _Hiroaki Yamanouchi_, Jul 07 2014

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Last modified August 4 13:49 EDT 2020. Contains 336201 sequences. (Running on oeis4.)