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%I #21 Apr 16 2014 11:20:18
%S 11,13,17,19,143,473,419645,17913329,27479459,4113856765,9696564647,
%T 17207135705,21202976255
%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}{sigma(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below).
%C a(14) > 3*10^10. - _Giovanni Resta_, Apr 16 2014
%e If n = 473, starting from the most significant digit, let us cut the number into the set 4, 47. We have:
%e sigma(4) = 7;
%e sigma(47) = 48
%e and 7 + 48 = 55 = sigma(473) - 473.
%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 sigma(n)-n=a then print(n); fi; od; end: P(10^9);
%Y Cf. A000203, A240894-A240898, A240900, A240902.
%K nonn,base,more
%O 1,1
%A _Paolo P. Lava_, Apr 14 2014
%E a(7)-a(13) from _Giovanni Resta_, Apr 16 2014
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