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A085612 Triangle in which the n-th row contains n numbers (beginning with the smallest unused value) that have the same prime signature as the first entry on that row.

%I A085612 #15 Apr 25 2021 03:28:57
%S A085612 1,2,3,4,9,25,5,7,11,13,6,10,14,15,21,8,27,125,343,1331,2197,12,18,20,
%T A085612 28,44,45,50,16,81,625,2401,14641,28561,83521,130321,17,19,23,29,31,
%U A085612 37,41,43,47,22,26,33,34,35,38,39,46,51,55,24,40,54,56,88,104,135,136,152
%N A085612 Triangle in which the n-th row contains n numbers (beginning with the smallest unused value) that have the same prime signature as the first entry on that row.
%C A085612 Permutation of the natural numbers when the triangle is seen flattened, inverse = A226387, see also A224401. - _Reinhard Zumkeller_, Jun 05 2013
%H A085612 Rémy Sigrist, <a href="/A085612/b085612.txt">Table of n, a(n) for n = 1..10011</a>
%H A085612 Rémy Sigrist, <a href="/A085612/a085612.gp.txt">PARI program for A085612</a>
%H A085612 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A085612 a(7) through a(10) = 5, 7, 11, 13 because 5 has not been used.
%e A085612 1;
%e A085612 2,3;
%e A085612 4,9,25;
%e A085612 5,7,11,13;
%e A085612 6,10,14,15,21;
%e A085612 8,27,125,343,1331,2197;
%e A085612 12,18,20,28,44,45,50;
%e A085612 16,81,625,2401,14641,28561,83521,130321;
%o A085612 (Haskell)
%o A085612 import Data.List ((\\))
%o A085612 a085612 n k = a085612_row n !! (k-1)
%o A085612 a085612_row n = a085612_tabf !! (n-1)
%o A085612 a085612_tabf = f 0 $ zip [1..] a046523_list where
%o A085612    f x zs'@(z:zs) = (map fst ys) : f (x + 1) (zs' \\ ys) where
%o A085612      ys = z : take x (filter ((== snd z) . snd) zs)
%o A085612 a085612_list = concat a085612_tabf
%o A085612 -- _Reinhard Zumkeller_, Jun 05 2013
%o A085612 (PARI) See Links section.
%Y A085612 Cf. A025487, A064839, A077558.
%Y A085612 Cf. A085836.
%Y A085612 Cf. A046523.
%K A085612 nonn,tabl
%O A085612 1,2
%A A085612 _Alford Arnold_, Jul 04 2003
%E A085612 More terms from _Ray Chandler_, Aug 21 2003