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A061827
Number of partitions of n into parts which are the digits of n.
9
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 5, 4, 4, 3, 3, 3, 3, 1, 11, 1, 4, 7, 3, 5, 2, 4, 2, 1, 11, 6, 1, 3, 3, 7, 2, 2, 5, 1, 11, 11, 4, 1, 3, 4, 2, 7, 2, 1, 11, 6, 4, 3, 1, 2, 2, 2, 2, 1, 11, 11, 11, 6, 3, 1, 2, 3, 4, 1, 11, 6, 4, 3, 3, 2, 1, 2, 2, 1, 11, 11, 4, 11, 3, 4, 2, 1, 2, 1, 11, 6, 11, 3, 3, 6, 2, 2
OFFSET
1,12
COMMENTS
a(A125289(n)) = 1, a(A125290(n)) > 1.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..15000 (first 1250 terms from Reinhard Zumkeller)
EXAMPLE
For n = 11, 1+1+1+1+1+1+1+1+1+1+1. so a(11) = 1. For n = 12, 2+2+2+2+2+2 = 2+2+1+1+1+1+1+1+1+1 = ...etc
a(20) = 1: the only partitions permitted use the digits 0 and 2, so there is just 1, 20 = 2+2+2... ten times.
MATHEMATICA
Length[IntegerPartitions[#, All, DeleteDuplicates@DeleteCases[IntegerDigits[#], 0]]]&/@Range[200] (* Sander G. Huisman, Nov 14 2022 *)
PROG
(Haskell)
import Data.List (sort, nub)
import Data.Char (digitToInt)
a061827 n =
p n (map digitToInt $ nub $ sort $ filter (/= '0') $ show n) where
p _ [] = 0
p 0 _ = 1
p m ds'@(d:ds)
| m < d = 0
| otherwise = p (m - d) ds' + p m ds
-- Reinhard Zumkeller, Aug 01 2011
CROSSREFS
KEYWORD
nonn,base,easy,look
AUTHOR
Amarnath Murthy, May 28 2001
EXTENSIONS
More terms from David Wasserman, Jul 29 2002
STATUS
approved