cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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).

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%I A328009 #27 Oct 09 2019 10:04:17
%S A328009 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,
%T A328009 74,148,296,592,1184,1,2,5,10,11,22,55,110,121,242,605,1210,1,2,4,5,
%U A328009 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
%N 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).
%C A328009 Row sums give a sequence formed by the terms of A180164 repeated as follows: 504, 504, 2394, 2394, 5544, 5544, ...
%e A328009 Array begins:
%e A328009 1, 2, 4,  5,  10,  11,  20,  22,   44,  55,   110,  220;
%e A328009 1, 2, 4, 71, 142, 284;
%e A328009 1, 2, 4,  8,  16,  32,  37,  74,  148,  296,  592, 1184;
%e A328009 1, 2, 5, 10,  11,  22,  55, 110,  121,  242,  605, 1210;
%e A328009 1, 2, 4,  5,  10,  20, 131, 262,  524,  655, 1310, 2620;
%e A328009 1, 2, 4, 17,  34,  43,  68,  86,  172,  731, 1462, 2924;
%e A328009 1, 2, 4,  5,  10,  20, 251, 502, 1004, 1255, 2510, 5020;
%e A328009 1, 2, 4, 13,  26,  52, 107, 214,  428, 1391, 2782, 5564,
%e A328009 1, 2, 4,  8,  19,  38,  41,  76,   82,  152,  164,  328, 779, 1558, 3116, 6232;
%e A328009 1, 2, 4,  8,  16,  32, 199, 398,  796, 1592, 3184, 6368;
%e A328009 ...
%t A328009 With[{s = Array[{#, DivisorSigma[1, #] - #} &, 6000]}, Flatten@ Divisors@ DeleteDuplicates[Sort /@ Select[Reverse /@ s, And[! FreeQ[s, #], UnsameQ @@ #] &]]] (* _Michael De Vlieger_, Oct 08 2019 *)
%Y A328009 Right border gives A259180 (amicable pairs).
%Y A328009 The length of row n is A328043(n).
%Y A328009 Column 1 gives A000012.
%Y A328009 Cf. A002025, A002046, A018339, A018373, A027750, A180164, A328063, A328064,  A328065.
%K A328009 nonn,tabf
%O A328009 1,2
%A A328009 _Omar E. Pol_, Oct 01 2019