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A213212
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Number of distinct products i*j*k over all triples (i,j,k) with i,j,k >= 0 and i+j+k <= n and gcd(i,j,k) <= 1.
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7
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1, 1, 1, 2, 3, 5, 6, 10, 12, 17, 20, 26, 29, 38, 44, 52, 59, 72, 78, 94, 104, 118, 130, 149, 160, 182, 198, 221, 237, 263, 278, 308, 330, 361, 383, 416, 438, 480, 509, 546, 574, 620, 646, 699, 734, 777, 816, 872, 907, 969, 1012, 1071, 1117, 1190, 1233, 1307, 1361
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OFFSET
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0,4
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COMMENTS
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This sequence is in reply to an extension request made in A100450.
Note that gcd(0,m) = m for any m.
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LINKS
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FORMULA
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MAPLE
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h:= proc() true end:
b:= proc(n) local c, i, j, p;
c:=0;
for i to iquo(n, 3) do
for j from i to iquo(n-i, 2) do
if igcd(i, j, n-i-j)=1 then p:= i*j*(n-i-j);
if h(p) then h(p):= false; c:=c+1 fi
fi
od
od; c
end:
a:= proc(n) a(n):= `if`(n=0, 1, a(n-1) +b(n)) end:
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MATHEMATICA
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f[n_] := Length[ Union[ Flatten[ Table[ If[ i+j+k <= n&& GCD[i, j, k] <= 1, i*j*k, 0], {i, 0, n}, {j, 0, n}, {k, 0, n}], 2]]]; Table[ f[n], {n, 0, 200}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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