A169901 Earliest sequence such that (x+y) | a(xy) for all x>=1, y>=1.

2, 3, 4, 20, 6, 35, 8, 18, 30, 77, 12, 728, 14, 45, 16, 680, 18, 1881, 20, 252, 110, 299, 24, 3850, 130, 135, 84, 5104, 30, 75361, 32, 396, 238, 665, 36, 28860, 38, 273, 80, 82082, 42, 218569, 44, 360, 2898, 1175, 48, 193648, 350, 2295, 260, 25228, 54, 33495

Offset: 1

Author

Andrew Weimholt, Jul 05 2010

Keywords

• nonn
• nice

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Programs

Maple

a:= n-> ilcm(seq(d+n/d, d=numtheory[divisors](n))):
seq(a(n), n=1..60);  # Alois P. Heinz, Mar 09 2016

Mathematica

eq[n_] := And @@ Table[y = n/x; Mod[a[x*y], x + y] == 0, {x, Divisors[n]}]; r[n_] := Reduce[ eq[n], a[n], Integers] /. C[1] -> 1; Table[a[n] /. ToRules[r[n]], {n, 1, 51}] (* Jean-François Alcover, Aug 03 2012 *)