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A269309 Consider the Euler totient function of a number x. Take the sum of its digits. Repeat the process deleting the first addendum and adding the previous sum. The sequence lists the numbers that after some iterations reach x.

%I A269309 #13 May 21 2019 22:24:37
%S A269309 13,21,63,177,206,412,655,824,1990,2637,11438,12485,23846,34132,40528,
%T A269309 56202,87539,94597,1288999,3075239,3106991,20689503,31173397,46230492,
%U A269309 65889985,79476719,170859904,266368503,295845211,420471958,445169688,797687940,962257660
%N A269309 Consider the Euler totient function of a number x. Take the sum of its digits. Repeat the process deleting the first addendum and adding the previous sum. The sequence lists the numbers that after some iterations reach x.
%e A269309 phi(13) = 12 : 1 + 2 = 3; 2 + 3 = 5; 3 + 5 = 8; 5 + 8 = 13.
%p A269309 with(numtheory): P:=proc(q,h) local a,b,k,n,t,v; v:=array(1..h);
%p A269309 for n from 2 to q do a:=phi(n); b:=ilog10(a)+1; if b>1 then
%p A269309 for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b);
%p A269309 while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
%p A269309 if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000);
%t A269309 Select[Range[10^5], EulerPhi[#] >= 10 && (d = IntegerDigits[EulerPhi[#]]; While[Total[d] < #, d = Join[Rest[d], {Total[d]}];]; Total[d] == #) &] (* _Robert Price_, May 21 2019 *)
%Y A269309 Cf. A000010, A007629, A269307, A269308, A269310, A269311, A269312.
%K A269309 nonn,base
%O A269309 1,1
%A A269309 _Paolo P. Lava_, Feb 24 2016
%E A269309 a(19)-a(33) from _Lars Blomberg_, Jan 18 2018