A377812 Number of quadruples of positive integers (x,y,a,b) such that a < b, gcd(a,b) = gcd(x,y) = 1 and a*x + b*y = n.
0, 0, 1, 2, 5, 4, 11, 9, 15, 12, 27, 14, 37, 22, 32, 31, 59, 26, 71, 38, 58, 48, 97, 42, 99, 62, 93, 68, 141, 48, 157, 91, 120, 94, 150, 78, 207, 112, 154, 108, 241, 84, 259, 138, 170, 150, 295, 116, 289, 144, 232, 178, 353, 136, 304, 188, 274, 210, 413, 132
Offset: 1
Keywords
Programs
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PARI
a(n)={sum(b=2, n-1, sum(y=1, (n-1)\b, my(s=n-b*y); sumdiv(s, a, aAndrew Howroyd, Nov 10 2024 -
PARI
seq(n)={my(v=Vec(sum(k=1, n-1, numdiv(k)*x^k, O(x^n))^2, -n), u=vector(n, n, moebius(n))); dirmul(dirmul(u,u), vector(#v, n, v[n]+numdiv(n)-sigma(n))/2)} \\ Andrew Howroyd, Nov 10 2024 -
Python
def a(n): count = 0 for a in range(1, n+1): for b in range(a + 1, n+1): if gcd(a, b) == 1: for x in range(1, n+1): for y in range(1, n+1): if gcd(x, y) == 1 and a * x + b * y == n: count += 1 return count print([a(n) for n in range(1,21)]) -
Python
from math import gcd from sympy import divisors def A377812(n): return sum(1 for ax in range(1,n-1) for a in divisors(ax,generator=True) for b in divisors(n-ax,generator=True) if aChai Wah Wu, Dec 11 2024
Formula
Moebius transform of A274108. - Andrew Howroyd, Nov 10 2024
Extensions
a(21) onwards from Andrew Howroyd, Nov 10 2024
Comments