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

0,2

Comments

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

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = Sum_{prime p < 10^n} floor(min(p^2,10^n)/p)*p = A024924(10^n) + A081738(r) - Sum_{prime p <= r} floor(10^n/p)*p = A046731(n) + A136021(n) + A081738(r) - Sum_{prime p <= r} floor(10^n/p)*p, where r = floor(10^(n/2)). - Max Alekseyev, Jun 20 2026

Example

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

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}]

Prog

(PARI) a(n) = sum(m=1, 10^n, sumdiv(m, d, d*isprime(d)*(d>=sqrt(m)))); \\ Michel Marcus, Jul 07 2014
(PARI) a108298(n) = my(s=0); forprime(p=2, 10^n, s += min(p^2, 10^n)\p*p); s; \\ Max Alekseyev, Jun 19 2026

Crossrefs

Cf. A024924, A046731, A081738, A097975, A136021.

Sequence in context: A089550 A007804 A295588 * A202384 A202369 A042743

Adjacent sequences: A108295 A108296 A108297 * A108299 A108300 A108301

Keyword

more,nonn,changed

Author

Ryan Propper, Jul 24 2005

Extensions

a(2)-a(7) and the example corrected and a(8)-a(14) from Hiroaki Yamanouchi, Jul 07 2014

Status

approved