A066418 Numbers k for which phi(k) + anti-phi(k) = k.

2, 3, 4, 5, 6, 7, 8, 12, 15, 27, 30, 40, 44, 57, 117, 128, 171, 236, 399, 408, 510, 1623, 3597, 3915, 4616, 4684, 7335, 10197, 10768, 14144, 32768, 39387, 76035, 77097, 106605, 162450, 196080, 219966, 391696

Offset

1,1

Comments

Anti-phi(n) (A066452) is the number of numbers coprime to all the anti-divisors of n.

See A066272 for definition of anti-divisor.

Links

Table of n, a(n) for n=1..39.

Jon Perry, Anti-phi function [Wayback Machine link]

Jon Perry, The Anti-divisor [Cached copy]

Jon Perry, The Anti-divisor: Even More Anti-Divisors [Cached copy]

Example

The anti-divisors of 7 are 1, 2, 3 and 5. Therefore of the integer 1-6, only 1 is coprime to 2, 3 and 5, therefore anti-phi(7)=1. phi(7)=6, therefore anti-phi(7)+phi(7)=7

Crossrefs

Cf. A066416, A066417, A058838, A066241, A066272, A066452.

Sequence in context: A342044 A238084 A211202 * A361437 A015845 A030702

Adjacent sequences: A066415 A066416 A066417 * A066419 A066420 A066421

Keyword

nonn,more

Author

Jon Perry, Dec 28 2001

Extensions

a(21)-a(34) from Nathaniel Johnston, Apr 20 2011

a(35)-a(39) from Amiram Eldar, Jan 12 2020

Status

approved