A240901 - OEIS

%I #12 Apr 16 2014 11:21:02

%S 16566,767869500,8187453840

%N Consider a number of k digits n = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1). Sequence lists the numbers n such that phi(n) = Sum_{i=1..k-1}{sigma(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below)

%C a(4) > 3*10^10. - _Giovanni Resta_, Apr 15 2014

%e If n = 16566, starting from the most significant digit, let us cut the number into the set 1, 16, 165, 1656. We have:

%e sigma(1) = 1;

%e sigma(16) = 31;

%e sigma(165) = 288;

%e sigma(1656) = 4680

%e and 1 + 31 + 288 + 4680 = 5000 = phi(16566).

%p with(numtheory); P:=proc(q) local a,k,n;

%p for n from 2 to q do a:=0; k:=1; while trunc(n/10^k)>0 do a:=a+sigma(trunc(n/10^k)); k:=k+1; od;

%p if phi(n)=a then print(n); fi; od; end: P(10^9);

%Y Cf. A000010, A000203, A240894-A240900, A240902.

%K nonn,base,more

%O 1,1

%A _Paolo P. Lava_, Apr 14 2014

%E a(2)-a(3) from _Giovanni Resta_, Apr 15 2014