A114102 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

Offset: 1

Author

Reinhard Zumkeller, Feb 12 2006

Keywords

• nonn
• base

Comments

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

Examples

			a(10) = #{10, 5+5, 2+2+2+2+2, 10x1} = 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.
		

Links

• Eric Weisstein's World of Mathematics, Digital Root

Crossrefs

Cf. A010888.

A147706. [From Reinhard Zumkeller, Nov 11 2008]

A156144. [From Reinhard Zumkeller, Feb 05 2009]

Programs

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