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A256824 Reverse concatenation of distinct digits of all divisors of n in base 10.

%I A256824 #16 Jul 25 2025 20:27:59
%S A256824 1,21,31,421,51,6321,71,8421,931,5210,1,64321,31,7421,531,86421,71,
%T A256824 986321,91,54210,7321,21,321,864321,521,6321,97321,87421,921,653210,
%U A256824 31,864321,31,74321,7531,9864321,731,98321,931,854210,41,764321,431,421,95431,64321
%N A256824 Reverse concatenation of distinct digits of all divisors of n in base 10.
%C A256824 Concatenation of elements of set of all digits of all divisors of n in decreasing order in base 10.
%C A256824 There are precisely 512 distinct terms of this sequence - see A256825 (possible values of a(n) in increasing order).
%C A256824 Minimal term is 1, maximal term is 9876543210.
%C A256824 Numbers n such that a(n) = 1 are in A243534, numbers n such that a(n) = 9876543210 are in A095050.
%C A256824 See A256826 - the smallest numbers k such that a(k) = A256825(n).
%H A256824 Jaroslav Krizek, <a href="/A256824/b256824.txt">Table of n, a(n) for n = 1..100</a>
%e A256824 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 A256824 Table[FromDigits[Reverse[Union[Flatten[IntegerDigits[Divisors[n]]]]]],{n,100}] (* _Ivan N. Ianakiev_, Apr 14 2015 *)
%o A256824 (Magma) [Seqint(Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))): n in [1..100]];
%o A256824 (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 A256824 Cf. A009995, A095050, A243534, A256825, A256826.
%K A256824 nonn,base
%O A256824 1,2
%A A256824 _Jaroslav Krizek_, Apr 10 2015