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%I #14 Nov 23 2019 13:58:06
%S 1,2,3,10,19,20,30,40,50,4,60,70,18,46,80,90,100,13,5,6,64,61,28,72,
%T 102,104,62,23,41,7,110,42,120,103,106,105,109,107,130,8,29,32,140,
%U 150,108,14,160,170,180,9,190,200,201,202,83,205,210,148,204,11,22
%N Lexicographically earliest sequence of distinct positive integers such that for any n > 0, f(n) * f(a(n)) = f(n * a(n)) where f(m) is the product of the digits of m.
%C This sequence is a variant of A329804; both sequences share graphical features.
%C This sequence is a self-inverse permutation of the positive integers.
%C Keyword "look" added in view of the scatterplot of 110000 terms. - _N. J. A. Sloane_, Nov 23 2019
%H Rémy Sigrist, <a href="/A329850/b329850.txt">Table of n, a(n) for n = 1..21000</a>
%H Rémy Sigrist, <a href="/A329850/a329850.png">Scatterplot of the first 110000 terms</a>
%H Rémy Sigrist, <a href="/A329850/a329850_1.png">Scatterplot of (x, y) such that f(x)*f(y) = f(x*y) and x = 1..1000, y = 1..1000</a>
%H Rémy Sigrist, <a href="/A329850/a329850.txt">C program for A329850</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(a(n)) = n.
%e The first terms, alongside f(n), f(a(n)) and f(n*a(n)), are:
%e n a(n) f(n) f(a(n)) f(n*a(n))
%e -- ---- ---- ------- ---------
%e 1 1 1 1 1
%e 2 2 2 2 4
%e 3 3 3 3 9
%e 4 10 4 0 0
%e 5 19 5 9 45
%e 6 20 6 0 0
%e 7 30 7 0 0
%e 8 40 8 0 0
%e 9 50 9 0 0
%e 10 4 0 4 0
%e 11 60 1 0 0
%e 12 70 2 0 0
%e 13 18 3 8 24
%e 14 46 4 24 96
%o (C) See Links section.
%Y Cf. A007954, A329804.
%K nonn,base,look
%O 1,2
%A _Rémy Sigrist_, Nov 22 2019
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