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

1,2

Comments

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

Links

Table of n, a(n) for n=1..76.

Example

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;
...

Mathematica

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

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.

Sequence in context: A057762 A109511 A018339 * A128216 A299322 A365501

Adjacent sequences: A328006 A328007 A328008 * A328010 A328011 A328012

Keyword

nonn,tabf

Author

Omar E. Pol, Oct 01 2019

Status

approved