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

0,2

Links

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

Formula

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

Prog

(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

Crossrefs

Cf. A007425, A061201.

Sequence in context: A342899 A017769 A017716 * A282931 A210783 A221237

Adjacent sequences: A180362 A180363 A180364 * A180366 A180367 A180368

Keyword

nonn

Author

Andrew Lelechenko, Jan 19 2011

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

Status

approved