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A085307 a(1) = 1; for n > 1, concatenate distinct prime factors of n in decreasing order.

%I A085307 #13 Oct 10 2017 20:15:32
%S A085307 1,2,3,2,5,32,7,2,3,52,11,32,13,72,53,2,17,32,19,52,73,112,23,32,5,
%T A085307 132,3,72,29,532,31,2,113,172,75,32,37,192,133,52,41,732,43,112,53,
%U A085307 232,47,32,7,52,173,132,53,32,115,72,193,292,59,532,61,312,73,2,135,1132,67
%N A085307 a(1) = 1; for n > 1, concatenate distinct prime factors of n in decreasing order.
%C A085307 n and a(n) have the same parity.
%H A085307 Alois P. Heinz, <a href="/A085307/b085307.txt">Table of n, a(n) for n = 1..20000</a>
%F A085307 Algorithm:
%F A085307 1. factorize n;
%F A085307 2. order prime factors by decreasing size;
%F A085307 3. concatenate prime factors and interpret the result as a decimal number.
%e A085307 m = 100 = 2*2*5*5 -> {2,5} -> {5,2} -> 52 = a(100);
%e A085307 a(510510) = 1713117532, while A084317(510510) = 2357111317.
%p A085307 with(numtheory):
%p A085307 a:= n-> parse(cat(`if`(n=1, 1, sort([factorset(n)[]], `>`)[]))):
%p A085307 seq(a(n), n=1..100);  # _Alois P. Heinz_, May 02 2016
%t A085307 f[n_] := FromDigits[ Flatten[ IntegerDigits /@ Reverse[ Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]]]]; Table[ f[n], {n, 1, 70}]
%t A085307 Table[FromDigits[Flatten[IntegerDigits/@Reverse[FactorInteger[n][[All, 1]]]]],{n,90}] (* _Harvey P. Dale_, Oct 10 2017 *)
%Y A085307 In A084317 the order of factors is increasing.
%Y A085307 Cf. A084317, A084318, A084319, A085308, A085309, A084796, A084797.
%K A085307 base,look,nonn
%O A085307 1,2
%A A085307 _Labos Elemer_, Jun 27 2003
%E A085307 Edited by _Robert G. Wilson v_, Jul 15 2003