A098216 Nonprime numbers m for which cototient(m) is a decimal repdigit.

1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 21, 25, 27, 30, 35, 49, 60, 86, 90, 93, 120, 121, 145, 159, 172, 175, 195, 231, 245, 253, 279, 291, 327, 365, 497, 535, 559, 693, 703, 737, 886, 979, 981, 993, 1037, 1111, 1121, 1411, 1457, 1517, 1617, 1772, 1774, 2047, 2059

Offset: 1

Author

Labos Elemer, Oct 22 2004

Keywords

• nonn
• base

Comments

For any odd repdigit k, Goldbach's conjecture implies there are primes p, q with p + q = k + 1, and then (if p <> q) p*q is a term. - Robert Israel, Jul 26 2025

Examples

			For m=97002, m-totient(m)=66666.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A096503, A010785.

Programs

Maple

filter:= proc(n) local t,x;
  t:= n - numtheory:-phi(n);
  if t = 1 then return false fi;
  x:= t mod 10;
  t = x * (10^(ilog10(t)+1)-1)/9
end proc:
select(filter, [$1..3000]); # Robert Israel, Jul 25 2025

Mathematica

ta={{0}};Do[s=Length[Union[IntegerDigits[n-EulerPhi[n]]]]; If[Equal[s, 1]&&!PrimeQ[n], Print[{n, n-EulerPhi[n]}];ta=Append[ta, n]], {n, 1, 100000}];ta=Delete[ta, 1];ta-EulerPhi[ta]