A083251 -id:A083251 - cp's OEIS frontend

A083252 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.

5, 105, 315, 182835, 960075, 7838265, 4291166265

Offset: 1

Labos Elemer, May 07 2003

a(7), if it exists, is > 10^9. - Vaclav Kotesovec, Sep 06 2019

			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.

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

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}]

isok(n) = abs(n-2*eulerphi(n)-2*numdiv(n)+2) == 5; \\ Michel Marcus, Jul 29 2017

a(6) from Michel Marcus, Jul 29 2017

a(7) from Amiram Eldar, Feb 02 2025

A083253 Smallest number k for which abs(A045763(k) - A073757(k)) = n, i.e., signed difference of size of related and unrelated sets to k equals either n or -n.

Original entry on oeis.org

30, 1, 2, 3, 4, 5, 8, 7, 16, 21, 32, 11, 64, 13, 84, 27, 78, 17, 200, 19, 90, 57, 140, 23, 102, 69, 120, 435, 114, 29, 132, 31, 126, 93, 392, 81, 138, 37, 156, 49, 230, 41, 168, 43, 322, 129, 260, 47, 150, 77, 180, 795, 186, 53, 204, 95, 198, 885, 280, 59, 434, 61, 228, 183

Offset: 0

Labos Elemer, May 07 2003

nonn

a(258) > 10^5. - Michael De Vlieger, Jul 31 2017

			A045763(x) - A073757(x) = 0 is first satisfied at x = 30 = a(0).

Michael De Vlieger, Table of n, a(n) for n = 0..257

Cf. A000005, A000010, A045763, A073757, A083243-A083249, A083250, A083251, A083252.

With[{s = Table[Abs[n - 2 (DivisorSigma[0, n] + EulerPhi[n] - 1)], {n, 10^3}]}, TakeWhile[#, # > 0 &] &@ Flatten@ Map[FirstPosition[s, #] /. k_ /; MissingQ@ k -> 0 &, Range[0, Max@ s]]] (* Michael De Vlieger, Jul 31 2017 *)

a(n) = {my(k = 1); while (abs(k - 2*(numdiv(k) + eulerphi(k) - 1)) != n, k++); k;} \\ Michel Marcus, Aug 01 2017

a(n) = min{x; abs(A045763(x) - A073757(x)) = n}.

a(p) = p, for p prime.

cp's OEIS Frontend

A083252 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.

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