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 A345687 For 1<=x<=n, 1<=y<=n, write gcd(x,y) = u*x+v*y with u,v minimal; a(n) = n^4*s, where s is the population variance of the values of u. 12
 0, 3, 32, 112, 500, 944, 3072, 5872, 12168, 19004, 40552, 59031, 109992, 152872, 221900, 315420, 513266, 658163, 1006272, 1277375, 1675544, 2121979, 3036460, 3652047, 4848004, 5918355, 7505768, 9012071, 11937118, 13778600, 17866848, 21132736, 25249454, 29499603 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The factor n^4 is to ensure that a(n) is an integer. A345426(n) = n^2*mu where mu is the mean of the values of u. The population standard deviation sqrt(s) appears to grow linearly with n. LINKS Table of n, a(n) for n=1..34. PROG (Python) from statistics import pvariance from sympy.core.numbers import igcdex def A345687(n): return pvariance(n**2*u for u, v, w in (igcdex(x, y) for x in range(1, n+1) for y in range(1, n+1))) CROSSREFS Cf. A345426. Sequence in context: A197524 A107465 A319219 * A211224 A213845 A221464 Adjacent sequences: A345684 A345685 A345686 * A345688 A345689 A345690 KEYWORD nonn AUTHOR Chai Wah Wu, Jun 23 2021 STATUS approved

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Last modified February 22 04:44 EST 2024. Contains 370239 sequences. (Running on oeis4.)