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A240896
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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}{phi(Sum_{j=1..i}{d_(j)*10^(j-1)})} (see example below).
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2
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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If n = 4351, starting from the least significant digit, let us cut the number into the set 1, 51, 351. We have:
phi(1) = 1;
phi(51) = 32;
phi(351) = 216
and 1 + 32 + 216 = 249 = sigma(4351) - 4351.
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MAPLE
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with(numtheory); P:=proc(q) local a, k, n;
for n from 2 to q do a:=0; k:=1; while (n mod 10^k)<n do
a:=a+phi(n mod 10^k); k:=k+1; od;
if sigma(n)-n=a then print(n); fi; od; end: P(10^9);
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CROSSREFS
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KEYWORD
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nonn,more,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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