login
A180365
Partial sums up to 10^n of A007425.
3
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
Sequence in context: A342899 A017769 A017716 * A282931 A210783 A221237
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