A083252 - OEIS

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, 407679713475, 12184942233849, 55340231370725130435, 1762426649044233290115, 29628967383206752924035, 1019212520795873860387065

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..13.

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, A083253.

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

a(8)-a(13) from Max Alekseyev, Nov 13 2025

STATUS

approved