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 A345725 For 1<=x<=n, 1<=y<=n with gcd(x,y)=1, write 1 = gcd(x,y) = u*x+v*y with u,v minimal; a(n) = m^2*s, where s is the population variance of the values of u+v and m is the number of such values. 1
 0, 0, 10, 28, 166, 224, 964, 1624, 3626, 4934, 12308, 15928, 33670, 42828, 62656, 85016, 154016, 181254, 301688, 364896, 480428, 580134, 901698, 1021274, 1412852, 1655336, 2149650, 2503910, 3518644, 3847556, 5247764, 6093004, 7339188, 8291404, 10135408, 11018524 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The factor m^2 is to ensure that a(n) is an integer. A345425(n) = m*mu where mu is the mean of the values of u+v. The population standard deviation sqrt(s) appears to grow linearly with n. LINKS Table of n, a(n) for n=1..36. PROG (Python) from statistics import pvariance from sympy.core.numbers import igcdex def A345725(n): zlist = [z for z in (igcdex(x, y) for x in range(1, n+1) for y in range(1, n+1)) if z[2] == 1] return pvariance(len(zlist)*(u+v) for u, v, w in zlist) CROSSREFS Cf. A345425, A345687, A345688, A345689, A345690, A345691, A345692, A345693, A345694, A345695. Sequence in context: A003665 A332432 A219812 * A185985 A358986 A239477 Adjacent sequences: A345722 A345723 A345724 * A345726 A345727 A345728 KEYWORD nonn AUTHOR Chai Wah Wu, Jun 24 2021 STATUS approved

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Last modified May 22 11:26 EDT 2024. Contains 372745 sequences. (Running on oeis4.)