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

1,1

Comments

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

Links

Table of n, a(n) for n=1..7.

Example

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.

Mathematica

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}]

Prog

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

Crossrefs

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

Sequence in context: A156848 A057016 A193340 * A327273 A034225 A273966

Adjacent sequences: A083249 A083250 A083251 * A083253 A083254 A083255

Keyword

nonn,more

Author

Labos Elemer, May 07 2003

Extensions

a(6) from Michel Marcus, Jul 29 2017

a(7) from Amiram Eldar, Feb 02 2025

Status

approved