editing

approved

a(10) = #{10, 5+5, 2+2+2+2+2, 1+1+1+1+1+1+1+1+1+110x1} = 4.;

a(11) = #{11, 10+1, 11x1} = 3;

a(12) = #{12, 10+1+1, 6+6, 4+4+4, 3+3+3+3, 2+2+2+2+2+2, 12x1} = 7.

(Haskell)

a114102 n = length $ filter (== 1) $

map (length . nub . (map a010888)) $ ps 1 n

where ps x 0 = [[]]

ps x y = [t:ts | t <- [x..y], ts <- ps t (y - t)]

-- Reinhard Zumkeller, Feb 04 2014

approved

editing

A147706. [From _Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Nov 11 2008]

A156144. [From _Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Feb 05 2009]

_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Feb 12 2006

A156144. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 05 2009]

nonn,base,new

A147706. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 11 2008]

nonn,base,new

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystemsgmail.com), Feb 12 2006

nonn,base,new

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Febr Feb 12 2006

Number of partitions of n such that all parts of a partition have the same digital root.

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 3, 7, 4, 5, 7, 6, 5, 8, 5, 8, 11, 8, 7, 16, 9, 10, 13, 12, 10, 22, 11, 15, 23, 16, 16, 26, 16, 18, 32, 22, 21, 41, 24, 27, 40, 28, 26, 55, 30, 36, 59, 40, 38, 65, 41, 45, 77, 48, 51, 95, 57, 60, 97, 66, 63, 119, 68, 80, 131, 89, 85, 150, 91, 96, 166, 104

1,2

a(n) = A116371(n) + A116372(n) + A116373(n) + A116374(n) + A116375(n) + A116376(n) + A116377(n) + A116378(n) + A114099(n).

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DigitalRoot.html">Digital Root</a>

a(10) = #{10, 5+5, 2+2+2+2+2, 1+1+1+1+1+1+1+1+1+1} = 4.

Cf. A010888.

nonn,base

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Febr 12 2006

approved