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A240899
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).
2
11, 13, 17, 19, 143, 473, 419645, 17913329, 27479459, 4113856765, 9696564647, 17207135705, 21202976255
OFFSET
1,1
COMMENTS
a(14) > 3*10^10. - Giovanni Resta, Apr 16 2014
EXAMPLE
If n = 473, starting from the most significant digit, let us cut the number into the set 4, 47. We have:
sigma(4) = 7;
sigma(47) = 48
and 7 + 48 = 55 = sigma(473) - 473.
MAPLE
with(numtheory); P:=proc(q) local a, k, n;
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;
if sigma(n)-n=a then print(n); fi; od; end: P(10^9);
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Paolo P. Lava, Apr 14 2014
EXTENSIONS
a(7)-a(13) from Giovanni Resta, Apr 16 2014
STATUS
approved