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A285890
The greater of the lexicographically least pair (x, y) such that 0 < x < y and sigma(x) = sigma(y) = n + x + y.
3
284, 75, 184, 615, 110, 435, 212, 585, 70, 195, 56, 30429, 1012, 915, 182, 297, 92, 16983, 1886, 1725, 250, 345, 182, 2415, 716, 2175, 130, 285, 506, 975, 78, 5145, 418, 1107, 225, 1305, 1504, 9275, 246, 2001, 1336, 35875, 2002, 6405, 322, 915, 176, 7315, 1292
OFFSET
0,1
LINKS
EXAMPLE
a(3) = 615: sigma(615) = sigma(390) = 615 + 390 + 3 = 1008;
a(4) = 110: sigma(110) = sigma(102) = 110 + 102 + 4 = 216;
a(5) = 435: sigma(435) = sigma(280) = 435 + 280 + 5 = 720.
MAPLE
with(numtheory): P:=proc(q) local a, b, k, n; for n from 0 to q do for k from 1 to q do
a:=sigma(k)-k-n; b:=sigma(a)-a-n; if a>0 and b=k and a<>b then print(a); break;
fi; od; od; end: P(10^9);
MATHEMATICA
Table[m = 1; While[MissingQ@ Set[k, SelectFirst[Range[m - 1], DivisorSigma[1, m] == DivisorSigma[1, #] == m + # + n &]], m++]; {k, m}, {n, 0, 10}][[All, -1]] (* Version 10.2, or *)
Do[m = 1; While[Set[k, Module[{k = 1}, While[! Xor[DivisorSigma[1, m] == DivisorSigma[1, k] == m + k + n, k >= m], k++]; k]] >= m, m++]; Print@ m, {n, 0, 10}] (* Michael De Vlieger, Apr 28 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Apr 28 2017
STATUS
approved