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%I #13 Nov 09 2015 19:35:40
%S 8,14,7,20,21,4,26,39,35,3,59,43,44,54,2,62,52,48,56,11,19,122,57,49,
%T 128,101,37,12,123,61,50,171,136,73,64,6,143,67,65,182,138,109,108,29,
%U 5,149,84,99,188,160,127,301,33,23,13,167,93,104,216,184,163,553,47,24,31,9,206,112,105,248,190,181,589,83,28,38,25,10,239
%N Infinite square array whose n-th row lists the numbers k for which A086793(k)=n, where A086793 = number of iteration of A034690 (sum of digits of divisors) to reach a fixed point, read by antidiagonals.
%C The fixed points of A034690 are 1 and 15, these are the only numbers not appearing in this table. All other positive integers appear exactly once.
%C Is there a simple explanation why row 7 seems to grow significantly faster than the neighboring rows?
%C From row 21 on, the terms become very large: cf. A094501 which is the first column with 15 prefixed.
%e The rows read
%e [ 8, 14, 20, 26, 59, 62, 122, 123, 143, 149, 167, 206, 239, 257, 293, 302,...],
%e [ 7, 21, 39, 43, 52, 57, 61, 67, 84, 93, 112, 124, 139, 151, 157, 189,...],
%e [ 4, 35, 44, 48, 49, 50, 65, 99, 104, 105, 116, 121, 125, 132, 140, 141,...],
%e [ 3, 54, 56, 128, 171, 182, 188, 216, 248, 252, 261, 264, 268, 270, 333, 387,...],
%e [ 2, 11, 101, 136, 138, 160, 184, 190, 208, 232, 238, 255, 282, 290, 318, 328,...],
%e [19, 37, 73, 109, 127, 163, 181, 271, 307, 396, 433, 523, 541, 613, 631, ...],
%e [12, 64, 108, 301, 553, 589, 949,1089,1197,1273,1687,1876,1957,2116, ...],
%e [ 6, 29, 33, 47, 83, 137, 173, 191, 227, 263, 281, 303, 317, ...],
%e [ 5, 23, 24, 28, 41, 42, 45, 92, 113, 131, 158, 164, ...],
%e [13, 31, 38, 60, 69, 74, 76, 77, 80, 86, 88, ...],
%e [ 9, 25, 72, 81, 117, 126, 156, 172, 258, 300, ...],
%e [10, 17, 22, 53, 71, 96, 107, 133, 202, ...], etc.
%e The first column is A094501.
%o (PARI) (f(k,N=20,a=[],n=0)=while(#a<N,A086793(n++)==k&&a=concat(a,n));a); T=vector(20,n,f(n,21-n)); for(n=1,20,for(k=1,n,print1(T[k][n-k+1]",")))
%Y Cf. A034690, A086793, A094501.
%K nonn,base,tabl
%O 1,1
%A _M. F. Hasler_, Nov 08 2015
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