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A299119
Positive solution to 2^(n-1) = (1/n) * Sum_{d|n} a(d) * a(n/d).
5
1, 2, 6, 14, 40, 84, 224, 484, 1134, 2480, 5632, 12036, 26624, 56896, 122640, 261078, 557056, 1176876, 2490368, 5237360, 11008704, 23057408, 48234496, 100635144, 209714400, 436154368, 905962860, 1878931264, 3892314112, 8052800160, 16642998272, 34359209436
OFFSET
1,2
COMMENTS
For prime p, a(p) = 2^(p-2)*p. - Jon E. Schoenfield, Feb 03 2018
LINKS
MAPLE
with(numtheory):
a:= proc(n) option remember; `if`(n=1, 1, n*2^(n-2)-
add(a(d)*a(n/d), d=divisors(n) minus {1, n})/2)
end:
seq(a(n), n=1..35); # Alois P. Heinz, Mar 07 2018
MATHEMATICA
nn=50;
sys=Table[2^(n-1)*n==Sum[a[d]*a[n/d], {d, Divisors[n]}], {n, nn}];
Array[a, nn]/.Solve[sys, Array[a, nn]][[2]]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 03 2018
STATUS
approved