A328009 Irregular array read by rows in which row n lists the divisors of the n-th term of the sequence of amicable pairs (A259180).

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220, 1, 2, 4, 71, 142, 284, 1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592, 1184, 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210, 1, 2, 4, 5, 10, 20, 131, 262, 524, 655, 1310, 2620, 1, 2, 4, 17, 34, 43, 68, 86, 172, 731, 1462, 2924, 1, 2, 4, 5, 10, 20, 251, 502, 1004, 1255

Offset: 1

Author

Omar E. Pol, Oct 01 2019

Keywords

• nonn
• tabf

Comments

Row sums give a sequence formed by the terms of A180164 repeated as follows: 504, 504, 2394, 2394, 5544, 5544, ...

Examples

			Array begins:
1, 2, 4,  5,  10,  11,  20,  22,   44,  55,   110,  220;
1, 2, 4, 71, 142, 284;
1, 2, 4,  8,  16,  32,  37,  74,  148,  296,  592, 1184;
1, 2, 5, 10,  11,  22,  55, 110,  121,  242,  605, 1210;
1, 2, 4,  5,  10,  20, 131, 262,  524,  655, 1310, 2620;
1, 2, 4, 17,  34,  43,  68,  86,  172,  731, 1462, 2924;
1, 2, 4,  5,  10,  20, 251, 502, 1004, 1255, 2510, 5020;
1, 2, 4, 13,  26,  52, 107, 214,  428, 1391, 2782, 5564,
1, 2, 4,  8,  19,  38,  41,  76,   82,  152,  164,  328, 779, 1558, 3116, 6232;
1, 2, 4,  8,  16,  32, 199, 398,  796, 1592, 3184, 6368;
...
		

Crossrefs

Right border gives A259180 (amicable pairs).

The length of row n is A328043(n).

Column 1 gives A000012.

Cf. A002025, A002046, A018339, A018373, A027750, A180164, A328063, A328064, A328065.

Programs

Mathematica

With[{s = Array[{#, DivisorSigma[1, #] - #} &, 6000]}, Flatten@ Divisors@ DeleteDuplicates[Sort /@ Select[Reverse /@ s, And[! FreeQ[s, #], UnsameQ @@ #] &]]] (* Michael De Vlieger, Oct 08 2019 *)