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.

8, 14, 7, 20, 21, 4, 26, 39, 35, 3, 59, 43, 44, 54, 2, 62, 52, 48, 56, 11, 19, 122, 57, 49, 128, 101, 37, 12, 123, 61, 50, 171, 136, 73, 64, 6, 143, 67, 65, 182, 138, 109, 108, 29, 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

Offset: 1

Author

M. F. Hasler, Nov 08 2015

Keywords

• nonn
• base
• tabl

Comments

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.

Is there a simple explanation why row 7 seems to grow significantly faster than the neighboring rows?

From row 21 on, the terms become very large: cf. A094501 which is the first column with 15 prefixed.

Examples

			The rows read
[ 8, 14,  20,  26,  59,  62, 122, 123, 143, 149, 167, 206, 239, 257, 293, 302,...],
[ 7, 21,  39,  43,  52,  57,  61,  67,  84,  93, 112, 124, 139, 151, 157, 189,...],
[ 4, 35,  44,  48,  49,  50,  65,  99, 104, 105, 116, 121, 125, 132, 140, 141,...],
[ 3, 54,  56, 128, 171, 182, 188, 216, 248, 252, 261, 264, 268, 270, 333, 387,...],
[ 2, 11, 101, 136, 138, 160, 184, 190, 208, 232, 238, 255, 282, 290, 318, 328,...],
[19, 37,  73, 109, 127, 163, 181, 271, 307, 396, 433, 523, 541, 613, 631, ...],
[12, 64, 108, 301, 553, 589, 949,1089,1197,1273,1687,1876,1957,2116, ...],
[ 6, 29,  33,  47,  83, 137, 173, 191, 227, 263, 281, 303, 317, ...],
[ 5, 23,  24,  28,  41,  42,  45,  92, 113, 131, 158, 164, ...],
[13, 31,  38,  60,  69,  74,  76,  77,  80,  86, 88, ...],
[ 9, 25,  72,  81, 117, 126, 156, 172, 258, 300, ...],
[10, 17,  22,  53,  71,  96, 107, 133, 202, ...], etc.
The first column is A094501.
		

Crossrefs

Cf. A034690, A086793, A094501.

Programs

PARI

(f(k,N=20,a=[],n=0)=while(#aA086793(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]",")))