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Reverse concatenation of distinct digits of all divisors of n in base 10.
11

%I #13 Sep 08 2022 08:46:12

%S 1,21,31,421,51,6321,71,8421,931,5210,1,64321,31,7421,531,86421,71,

%T 986321,91,54210,7321,21,321,864321,521,6321,97321,87421,921,653210,

%U 31,864321,31,74321,7531,9864321,731,98321,931,854210,41,764321,431,421,95431,64321

%N Reverse concatenation of distinct digits of all divisors of n in base 10.

%C Concatenation of elements of set of all digits of all divisors of n in decreasing order in base 10.

%C There are precisely 512 distinct terms of this sequence - see A256825 (possible values of a(n) in increasing order).

%C Minimal term is 1, maximal term is 9876543210.

%C Numbers n such that a(n) = 1 are in A243534, numbers n such that a(n) = 9876543210 are in A095050.

%C See A256826 - the smallest numbers k such that a(k) = A256825(n).

%H Jaroslav Krizek, <a href="/A256824/b256824.txt">Table of n, a(n) for n = 1..100</a>

%e For n = 12; list of divisors of 12 in base 10: 1, 2, 3, 4, 6, 12 contains five distinct digits (1, 2, 3, 4, 6) whose reverse concatenation is 64321.

%t Table[FromDigits[Reverse[Union[Flatten[IntegerDigits[Divisors[n]]]]]],{n,100}] (* _Ivan N. Ianakiev_, Apr 14 2015 *)

%o (Magma) [Seqint(Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))): n in [1..100]]

%o (PARI) a(n) = {my(v = []); fordiv(n, d, v = vecsort(concat(v, digits(d)),,8)); subst(Polrev(v), x, 10);} \\ _Michel Marcus_, Apr 11 2015

%Y Cf. A009995, A095050, A243534, A256825, A256826.

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, Apr 10 2015