cp's OEIS Frontend

A114102 Number of partitions of n such that all parts of a partition have the same digital root.

%I A114102 #8 Feb 16 2025 08:32:59
%S A114102 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,
%T A114102 11,15,23,16,16,26,16,18,32,22,21,41,24,27,40,28,26,55,30,36,59,40,38,
%U A114102 65,41,45,77,48,51,95,57,60,97,66,63,119,68,80,131,89,85,150,91,96,166,104
%N A114102 Number of partitions of n such that all parts of a partition have the same digital root.
%C A114102 a(n) = A116371(n) + A116372(n) + A116373(n) + A116374(n) + A116375(n) + A116376(n) + A116377(n) + A116378(n) + A114099(n).
%H A114102 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DigitalRoot.html">Digital Root</a>
%e A114102 a(10) = #{10, 5+5, 2+2+2+2+2, 10x1} = 4;
%e A114102 a(11) = #{11, 10+1, 11x1} = 3;
%e A114102 a(12) = #{12, 10+1+1, 6+6, 4+4+4, 3+3+3+3, 2+2+2+2+2+2, 12x1} = 7.
%o A114102 (Haskell)
%o A114102 a114102 n = length $ filter (== 1) $
%o A114102             map (length . nub . (map a010888)) $ ps 1 n
%o A114102    where ps x 0 = [[]]
%o A114102          ps x y = [t:ts | t <- [x..y], ts <- ps t (y - t)]
%o A114102 -- _Reinhard Zumkeller_, Feb 04 2014
%Y A114102 Cf. A010888.
%Y A114102 A147706. [From _Reinhard Zumkeller_, Nov 11 2008]
%Y A114102 A156144. [From _Reinhard Zumkeller_, Feb 05 2009]
%K A114102 nonn,base
%O A114102 1,2
%A A114102 _Reinhard Zumkeller_, Feb 12 2006