

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



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

0,2


COMMENTS

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


LINKS

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


EXAMPLE

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


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}]


PROG

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


CROSSREFS

Cf. A097974.
Sequence in context: A197448 A241127 A268551 * A295171 A254545 A160293
Adjacent sequences: A108271 A108272 A108273 * A108275 A108276 A108277


KEYWORD

nonn


AUTHOR

Ryan Propper, Jul 24 2005


EXTENSIONS

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


STATUS

approved



