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A187807
Numbers n that can be expressed as the sum of the arithmetic derivatives of k previous numbers starting from n for some k >= 1.
2
4, 5, 6, 7, 27, 42, 43, 1310, 3125, 47058, 47059, 151747, 192382, 192383, 244419, 257614, 823543, 28170538, 28170539, 36861843, 48647587, 556429758, 2736456639, 26781610526
OFFSET
1,1
COMMENTS
A051674 is a subsequence of this sequence.
FORMULA
n = Sum{j=1..k} (n-j+1)', for some k >= 1.
EXAMPLE
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.
MAPLE
with(numtheory);
A187807:= proc(i)
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:
A187807(100000000);
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Jan 07 2013
EXTENSIONS
a(22)-a(24) from Donovan Johnson, Jan 26 2013
STATUS
approved