cp's OEIS Frontend

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

%I A098216 #15 Jul 27 2025 11:36:44
%S A098216 1,4,6,8,9,10,12,14,15,16,21,25,27,30,35,49,60,86,90,93,120,121,145,
%T A098216 159,172,175,195,231,245,253,279,291,327,365,497,535,559,693,703,737,
%U A098216 886,979,981,993,1037,1111,1121,1411,1457,1517,1617,1772,1774,2047,2059
%N A098216 Nonprime numbers m for which cototient(m) is a decimal repdigit.
%C A098216 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
%H A098216 Robert Israel, <a href="/A098216/b098216.txt">Table of n, a(n) for n = 1..1000</a>
%e A098216 For m=97002, m-totient(m)=66666.
%p A098216 filter:= proc(n) local t,x;
%p A098216   t:= n - numtheory:-phi(n);
%p A098216   if t = 1 then return false fi;
%p A098216   x:= t mod 10;
%p A098216   t = x * (10^(ilog10(t)+1)-1)/9
%p A098216 end proc:
%p A098216 select(filter, [$1..3000]); # _Robert Israel_, Jul 25 2025
%t A098216 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]
%Y A098216 Cf. A096503, A010785.
%K A098216 nonn,base
%O A098216 1,2
%A A098216 _Labos Elemer_, Oct 22 2004