cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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).

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%I A108274 #13 Jul 20 2014 09:43:07
%S A108274 0,11,327,7714,184680,4617253,118697919,3149768778,85356405077,
%T A108274 2357169671137,66097467843823,1875931900135854,53804720498131760,
%U A108274 1556256544987695973,45343922927650954928,1329347125287604758708,39180941384720954859005
%N 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).
%C A108274 Does a(n+1)/a(n) converge?
%H A108274 Hiroaki Yamanouchi, <a href="/A108274/b108274.txt">Table of n, a(n) for n = 0..19</a>
%e A108274 The first 10^2 terms in A097974 sum to 327, so a(2) = 327.
%t A108274 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 A108274 (PARI) a(n) = sum(m=1, 10^n, sumdiv(m, d, d*isprime(d)*(d<=sqrt(m)))); \\ _Michel Marcus_, Jul 07 2014
%Y A108274 Cf. A097974.
%K A108274 nonn
%O A108274 0,2
%A A108274 _Ryan Propper_, Jul 24 2005
%E A108274 a(2)-a(7) and the example corrected and a(8)-a(16) from _Hiroaki Yamanouchi_, Jul 07 2014