A240895 - OEIS

%I #14 Jan 03 2024 10:01:38

%S 11,25,31,41,61,71,341,671,2119,10231,39579,52231,60341,402959,

%T 1288689,1393059,1956759,16752951,108659999,181704519,794033191,

%U 1062726071,3518397571,4062296851,4085227151,7015608139

%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)})} (see example below).

%C a(27) > 10^10. - _Giovanni Resta_, Apr 16 2014

%e If n = 52231, starting from the least significant digit, let us cut the number into the set 1, 31, 231, 2231. We have:

%e sigma(1) = 1;

%e sigma(31) = 32;

%e sigma(231) = 384;

%e sigma(2231) = 2352

%e and 1 + 32 + 384 + 2352 = 2769 = sigma(52231) - 52231.

%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); k:=k+1; od;

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

%Y Cf. A000203, A240894, A240896-A240902.

%K nonn,more,base

%O 1,1

%A _Paolo P. Lava_, Apr 14 2014

%E a(14), a(18)-a(26) from _Giovanni Resta_, Apr 16 2014