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%I #15 Apr 16 2014 09:02:20
%S 13,17,23,37,43,47,53,67,73,83,97,131,211,241,271,311,331,431,461,541,
%T 571,631,641,661,761,811,899,911,941,971,1601,3701,5101,5701,6101,
%U 6701,8101,9601,13001,19001,24001,54001,69001,93001,97001,102737,194357,217267
%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_(j)*10^(j-1)}) - Sum_{j=1..i}{d_(j)*10^(j-1)}} (see example below).
%C Mainly primes. The first composite numbers in the sequence are 899, 102737, 194357, 217267, 377149, etc.
%H Giovanni Resta, <a href="/A240894/b240894.txt">Table of n, a(n) for n = 1..135</a> (terms < 10^10)
%e If n = 194357, starting from the least significant digit, let us cut the number into the set 7, 57, 357, 4357, 94357. We have:
%e sigma(7) - 7 = 1;
%e sigma(57) - 57 = 23;
%e sigma(357) - 357 = 219;
%e sigma(4357) - 4357 = 1;
%e sigma(94357) - 94357 = 759
%e and 1 + 23 + 219 + 1 + 759 = 1003 = sigma(194357) - 194357.
%p with(numtheory); P:=proc(q) local a,k,n;
%p for n from 2 to q do a:=0; k:=1; while (n mod 10^k)<n do
%p a:=a+sigma(n mod 10^k)-(n mod 10^k); k:=k+1; od;
%p if sigma(n)-n=a then print(n); fi; od; end: P(10^9);
%Y Cf. A000203, A240895-A240902.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Apr 14 2014
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