OFFSET
1,1
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10082
A. Karttunen, Ratio a(n)/A263085(n) drawn with OEIS Plot2-script
FORMULA
a(1) = 2; for n > 1, a(n) = A000005(2*n) + a(n-1) [where A000005(k) gives the number of divisors of k].
Other identities. For all n >= 1:
a(n) ~ n/2 * (3*log(n) + log(2) + 6*gamma - 3), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Feb 13 2019
From Ridouane Oudra, Aug 24 2019: (Start)
a(n) = Sum_{k=1..n} A000005(2*k)
MAPLE
with(numtheory): seq(add(tau(2*k), k=1..n), n= 1..60); # Ridouane Oudra, Aug 24 2019
MATHEMATICA
Accumulate[DivisorSigma[0, 2 Range@ 69]] (* Michael De Vlieger, Oct 13 2015 *)
PROG
(Scheme, with memoization-macro definec)
(PARI) a(n) = sum(k=1, n, numdiv(2*k)); \\ Michel Marcus, Aug 25 2019
(Python)
from math import isqrt
def A263086(n): return (t:=isqrt(m:=n>>1))**2-((s:=isqrt(n))**2<<1)+((sum(n//k for k in range(1, s+1))<<1)-sum(m//k for k in range(1, t+1))<<1) # Chai Wah Wu, Oct 23 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 12 2015
STATUS
approved