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%I #19 Jan 03 2024 10:02:05
%S 11,12,35,38,57,59,152,599,2812,3419,3915,6733,11671,16706,16714,
%T 16858,25303,26752,128257,171762,238571,265872,345715,375923,486141,
%U 496975,573433,1492832,2324671,2944061
%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 Sum_{i=1..k-1}{sigma(Sum_{j=1..i}{d_(j)*10^(j-1)})} = Sum_{i=1..k-1}{phi(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below).
%e If n = 345715, starting from the least significant digit, let us cut the number into the set {5, 15, 715, 5715, 45715}. We have:
%e phi(5) = 4;
%e phi(15) = 8;
%e phi(715) = 480;
%e phi(5715) = 3024;
%e phi(45715) = 35520.
%e Then, starting from the most significant digit, let us cut the number into the set {3, 34, 345, 3457, 34571}. We have:
%e sigma(3) = 4;
%e sigma(34) = 54;
%e sigma(345) = 576;
%e sigma(3457) = 3458;
%e sigma(34571) = 34944.
%e Finally, 4 + 8 + 480 + 3024 + 35520 = 4 + 54 + 576 + 3458 + 34944 = 39036.
%p with(numtheory); P:=proc(q) local a, b, k, n; for n from 10 to q do
%p a:=0; k:=1; while trunc(n/10^k)>0 do a:=a+sigma(trunc(n/10^k)); k:=k+1; od;
%p b:=0; k:=1; while (n mod 10^k)<n do b:=b+phi(n mod 10^k); k:=k+1; od;
%p if a=b then print(n); fi; od; end: P(10^9);
%Y Cf. A000010, A000203, A240894-A240903, A241207, A241502, A241503, A244069.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Jun 19 2014
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