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A187215
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Sum of the elements of the absolute difference table of the divisors of n.
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11
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1, 4, 6, 11, 10, 21, 14, 26, 25, 31, 22, 52, 26, 45, 54, 57, 34, 82, 38, 82, 72, 73, 46, 119, 71, 87, 90, 108, 58, 161, 62, 120, 108, 115, 134, 181, 74, 129, 126, 193, 82, 221, 86, 172, 218, 157, 94, 252, 141, 190, 162, 204, 106, 285, 202, 233
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 2n, if n is prime.
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EXAMPLE
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For n = 14 the divisors of 14 are 1, 2, 7, 14, and the absolute difference triangle of the divisors is
1 . 2 . 7 . 14
. 1 . 5 . 7
. . 4 . 2
. . . 2
The sum of all elements of the triangle is 1 + 2 + 7 + 14 + 1 + 5 + 7 + 4 + 2 + 2 = 45, so a(14) = 45.
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MAPLE
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with(numtheory):
DD:= l-> [seq(abs(l[i]-l[i-1]), i=2..nops(l))]:
a:= proc(n) local l;
l:= sort([divisors(n)[]], `>`);
add(j, j=[seq((DD@@i)(l)[], i=0..nops(l)-1)]);
end:
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MATHEMATICA
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Table[Total@ Flatten@ NestWhileList[Abs@ Differences@ # &, Divisors@ n, Length@ # > 1 &], {n, 56}] (* Michael De Vlieger, May 18 2016 *)
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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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EXTENSIONS
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STATUS
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approved
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