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A187807
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Numbers n that can be expressed as the sum of the arithmetic derivatives of k previous numbers starting from n for some k >= 1.
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2
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4, 5, 6, 7, 27, 42, 43, 1310, 3125, 47058, 47059, 151747, 192382, 192383, 244419, 257614, 823543, 28170538, 28170539, 36861843, 48647587, 556429758, 2736456639, 26781610526
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OFFSET
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1,1
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COMMENTS
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A051674 is a subsequence of this sequence.
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LINKS
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FORMULA
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n = Sum{j=1..k} (n-j+1)', for some k >= 1.
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EXAMPLE
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k=1: n=27 -> 27 = 27'.
k=2: n=1310 -> 1310 = 1310'+1309' = 927+383.
k=3: n=43 -> 43 = 43'+42'+41' = 1+41+1.
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MAPLE
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with(numtheory);
local a, b, c, n.p;
for n from 4 to i do
a:=0; b:=-1;
while a<n do b:=b+1; a:=a+(n-b)*add(op(2, p)/op(1, p), p=ifactors(n-b)[2]); od;
if a=n then print(n); fi; od; end:
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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