cp's OEIS Frontend

A260059 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.

%I A260059 #13 Nov 09 2015 19:35:40
%S A260059 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 A260059 128,101,37,12,123,61,50,171,136,73,64,6,143,67,65,182,138,109,108,29,
%U A260059 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 A260059 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 A260059 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 A260059 Is there a simple explanation why row 7 seems to grow significantly faster than the neighboring rows?
%C A260059 From row 21 on, the terms become very large: cf. A094501 which is the first column with 15 prefixed.
%e A260059 The rows read
%e A260059 [ 8, 14,  20,  26,  59,  62, 122, 123, 143, 149, 167, 206, 239, 257, 293, 302,...],
%e A260059 [ 7, 21,  39,  43,  52,  57,  61,  67,  84,  93, 112, 124, 139, 151, 157, 189,...],
%e A260059 [ 4, 35,  44,  48,  49,  50,  65,  99, 104, 105, 116, 121, 125, 132, 140, 141,...],
%e A260059 [ 3, 54,  56, 128, 171, 182, 188, 216, 248, 252, 261, 264, 268, 270, 333, 387,...],
%e A260059 [ 2, 11, 101, 136, 138, 160, 184, 190, 208, 232, 238, 255, 282, 290, 318, 328,...],
%e A260059 [19, 37,  73, 109, 127, 163, 181, 271, 307, 396, 433, 523, 541, 613, 631, ...],
%e A260059 [12, 64, 108, 301, 553, 589, 949,1089,1197,1273,1687,1876,1957,2116, ...],
%e A260059 [ 6, 29,  33,  47,  83, 137, 173, 191, 227, 263, 281, 303, 317, ...],
%e A260059 [ 5, 23,  24,  28,  41,  42,  45,  92, 113, 131, 158, 164, ...],
%e A260059 [13, 31,  38,  60,  69,  74,  76,  77,  80,  86, 88, ...],
%e A260059 [ 9, 25,  72,  81, 117, 126, 156, 172, 258, 300, ...],
%e A260059 [10, 17,  22,  53,  71,  96, 107, 133, 202, ...], etc.
%e A260059 The first column is A094501.
%o A260059 (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 A260059 Cf. A034690, A086793, A094501.
%K A260059 nonn,base,tabl
%O A260059 1,1
%A A260059 _M. F. Hasler_, Nov 08 2015