A116371 -id:A116371 - cp's OEIS frontend

A147706 Number of partitions of n into parts having distinct digital roots (A010888).

1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 11, 15, 16, 20, 25, 28, 32, 39, 46, 50, 62, 66, 78, 93, 101, 112, 132, 150, 161, 192, 202, 232, 268, 287, 312, 361, 400, 425, 497, 516, 582, 658, 698, 748, 858, 932, 982, 1135, 1164, 1296, 1443, 1519, 1610, 1845, 1968, 2059, 2360, 2395

Offset: 1

Reinhard Zumkeller, Nov 11 2008

a(n) <= A000009(n).

Likely a duplicate of A114098. [From R. J. Mathar, Dec 13 2008]

			A000009(16) = 32, in which the following 4 partitions
contain parts with common digital roots:
12 + 3 + 1, 11 + 3 + 2, 10 + 5 + 1 and 10 + 3 + 2 + 1,
therefore a(16) = 32 - 4 = 28.

A114102, A116371, A116372, A116373, A116374, A116375, A116376, A116377, A116378, A114099.

A156144 Number of partitions of n into parts having in decimal representation the same digital root as n has.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 3, 2, 3, 1, 1, 2, 1, 1, 3, 5, 2, 5, 1, 1, 2, 1, 1, 5, 8, 4, 8, 2, 1, 4, 1, 1, 7, 13, 5, 13, 2, 2, 5, 1, 1, 11, 20, 9, 19, 3, 2, 9, 1, 1, 15, 31, 12, 29, 4, 3, 11, 2, 1, 22, 46, 20, 42, 7, 4, 18, 2, 2, 30, 68, 27, 61, 9, 6, 23, 3, 2, 42, 98, 42, 85

Offset: 1

Reinhard Zumkeller, Feb 05 2009

a(n) <= a(n+9); Max{n: a(n)=1} = 71;
A156145 and A017173 give record values and where they occur: a(A017173(n-1))=A156145(n);
a(A017173(n)) = A116371(A017173(n)).

			a(19) = #{19, 10+1+1+1+1+1+1+1+1+1, 19x1} = 3;
a(20) = #{20, 2+2+2+2+2+2+2+2+2+2} = 2;
a(21) = #{21, 3+3+3+3+3+3+3, 12+3+3+3} = 3;
a(22) = #{22} = 1;

R. Zumkeller, Table of n, a(n) for n = 1..500

A010888, A114102.

a156144 n = p [x | x <- [1..n], a010888 x == a010888 n] n where
   p _  0 = 1
   p [] _ = 0
   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
-- Reinhard Zumkeller, Feb 04 2014

cp's OEIS Frontend

A147706 Number of partitions of n into parts having distinct digital roots (A010888).

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