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URL: https://oeis.org/A270383

⇱ A270383 - OEIS

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A270383
Number of ordered pairs (i,j) with i >= j, |i|, |j| <= n, and |i * j| <= n.
1
1, 6, 12, 18, 27, 33, 43, 49, 59, 68, 78, 84, 98, 104, 114, 124, 137, 143, 157, 163, 177, 187, 197, 203, 221, 230, 240, 250, 264, 270, 288, 294, 308, 318, 328, 338, 359, 365, 375, 385, 403, 409, 427, 433, 447, 461, 471, 477, 499, 508, 522
OFFSET
0,2
LINKS
FORMULA
a(n) = 2*(Sum_{k=1..n} tau(k)) + floor(sqrt(n)) + 2*n + 1, where tau(k) = A000005(k) is number of divisors of k.
a(n) = A067274(n) + 2 for n >= 1.
EXAMPLE
For n = 2 the a(2) = 12 pairs are (2,1), (2,0), (2,-1), (1,1), (1,0), (1,-1), (1,-2), (0,0), (0,-1), (0,-2), (-1,-1), and (-1,-2). - Danny Rorabaugh, Apr 05 2016
MATHEMATICA
a[n_]:=2Sum[Length[Divisors[k]], {k, 1, n}]+Floor[Sqrt[n]]+2n+1
PROG
(PARI) a(n) = 2*sum(k=1, n, numdiv(k)) + sqrtint(n) + 2*n + 1; \\ Michel Marcus, Apr 05 2016
(Python)
from math import isqrt
def A270383(n): return (n-(s:=isqrt(n))**2+(sum(n//k for k in range(1, s+1))<<1)<<1)+s+1 if n else 1 # Chai Wah Wu, Jan 27 2026
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved