%I #27 Nov 22 2025 16:37:03

%S 5,105,315,182835,960075,7838265,4291166265,407679713475,

%T 12184942233849,55340231370725130435,1762426649044233290115,

%U 29628967383206752924035,1019212520795873860387065

%N Numbers k for which abs(A045763(k) - A073757(k)) = 5, i.e., signed difference of size of related and unrelated sets to k equals either 5 or -5.

%e For k = 960075: d = 36 divisors, r = 480000 coprimes, u = 480040 unrelated; k - u = r + d - 1 = 480035 related numbers to k; thus abs(480040 - 480035) = 5.

%t Do[r=EulerPhi[n]; d=DivisorSigma[0, n]; u=n-r-d+1; df=2*u-n; If[Equal[Abs[df], 5], Print[n(*, {d, r, u}*)]], {n, 1, 3000}]

%o (PARI) isok(n) = abs(n-2*eulerphi(n)-2*numdiv(n)+2) == 5; \\ _Michel Marcus_, Jul 29 2017

%Y Cf. A000005, A000010, A045763, A073757, A083243-A083249, A083250, A083251, A083253.

%K nonn,more

%O 1,1

%A _Labos Elemer_, May 07 2003

%E a(6) from _Michel Marcus_, Jul 29 2017

%E a(7) from _Amiram Eldar_, Feb 02 2025

%E a(8)-a(13) from _Max Alekseyev_, Nov 13 2025