A299119 Positive solution to 2^(n-1) = (1/n) * Sum_{d|n} a(d) * a(n/d).

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

Author

Gus Wiseman, Feb 03 2018

Keywords

• nonn

Comments

For prime p, a(p) = 2^(p-2)*p. - Jon E. Schoenfield, Feb 03 2018

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000010, A000740, A001787, A018804, A023900, A029935, A034691, A046643, A059966, A228369, A257098, A296302, A298971, A299149, A299151.

Programs

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]]