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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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]]

CROSSREFS

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

Sequence in context: A263735 A263731 A293742 * A271895 A151538 A284998

Adjacent sequences:  A299116 A299117 A299118 * A299120 A299121 A299122

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 03 2018

STATUS

approved

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Last modified August 3 08:21 EDT 2021. Contains 346435 sequences. (Running on oeis4.)