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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 sigma(n) - n = Sum_{i=1..k-1}{phi(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below).
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%I #15 Apr 16 2014 11:20:43

%S 11,13,17,19,23,29,1363,2983,23389,101299,132011,136363,144133,198169,

%T 1076441,1222423,1973987,2185367,2191463,2673623,11491523,18160663,

%U 127666453,262001569,264484657,2080368463,2763449953,20603271407,28272595783

%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 sigma(n) - n = Sum_{i=1..k-1}{phi(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below).

%e If n = 132011, starting from the most significant digit, let us cut the number into the set 1, 13, 132, 1320, 13201. We have:

%e phi(1) = 1;

%e phi(13) = 12;

%e phi(132) = 40;

%e phi(1320) = 320;

%e phi(13201) = 12852

%e and 1 + 12 + 40 + 320 + 12852 = 13225 = sigma(132011) - 132011.

%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+phi(trunc(n/10^k)); k:=k+1; od;

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

%Y Cf. A000010, A000203, A240894-A240899, A240901, A240902.

%K nonn,base,more

%O 1,1

%A _Paolo P. Lava_, Apr 14 2014

%E a(15)-a(29) from _Giovanni Resta_, Apr 15 2014