A180365 Partial sums up to 10^n of A007425.

1, 53, 1471, 29425, 496623, 7518850, 106030594, 1421760251, 18362473634, 230375375227, 2824280446479, 33978264556380, 402439152166882, 4703975577244852, 54365786164534232, 622220063695532731, 7060841638683030355, 79525016215415440837

Offset: 0

Author

Andrew Lelechenko, Jan 19 2011

Keywords

• nonn

Links

• Henri Lifchitz, Table of n, a(n) for n = 0..23 (first 21 terms from Hiroaki Yamanouchi)

Crossrefs

Cf. A007425, A061201.

Programs

PARI

a(n)=sum(k=1, 10^n, numdiv(k)*floor((10^n)/k));
vector(7, n, a(n-1)) \\ Altug Alkan, Sep 24 2015

Python

from math import isqrt
from sympy import integer_nthroot
def A180365(n): return (m:=integer_nthroot(t:=10**n,3)[0])**3+3*sum(-(s:=isqrt(r:=t//i))**2+(sum(r//k for k in range(1,s+1))<<1)-sum(t//(i*j) for j in range(1,m+1)) for i in range(1,m+1)) # Chai Wah Wu, Oct 23 2023

Formula

a(n) = A061201(10^n).

Extensions

One more term (a(16)) and typo in crossrefs fixed by Andrew Lelechenko, Apr 13 2011

a(17) from Hiroaki Yamanouchi, Jul 15 2014