cp's OEIS Frontend

A032451 Irregular triangle read by rows: there is a row for each value of n for which the aliquot sequence starting at n eventually reaches 1, giving the part of the sequence from n to 1.

%I A032451 #14 Dec 12 2014 23:58:21
%S A032451 1,2,1,3,1,4,3,1,5,1,7,1,8,7,1,9,4,3,1,10,8,7,1,11,1,12,16,15,9,4,3,1,
%T A032451 13,1,14,10,8,7,1,15,9,4,3,1,16,15,9,4,3,1,17,1,18,21,11,1,19,1,20,22,
%U A032451 14,10,8,7,1,21,11,1,22,14,10,8,7,1,23,1,24,36,55,17,1,26,16
%N A032451 Irregular triangle read by rows: there is a row for each value of n for which the aliquot sequence starting at n eventually reaches 1, giving the part of the sequence from n to 1.
%C A032451 Related to Catalan's conjecture about iterations of f(n) = sigma(n) - n.
%H A032451 L. Alaoglu and P. Erdős, <a href="http://dx.doi.org/10.1090/S0002-9904-1944-08257-8">A conjecture in elementary number theory</a>, Bull. Amer. Math. Soc. 50 (1944), 881-882.
%e A032451 The aliquot sequences starting with the numbers from 1 to 32 are as follows:
%e A032451 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [4, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, ...]
%e A032451 [7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [8, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [9, 4, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [10, 8, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [12, 16, 15, 9, 4, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] (A143090)
%e A032451 [13, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [14, 10, 8, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] (A143721)
%e A032451 [15, 9, 4, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] (A143090)
%e A032451 [16, 15, 9, 4, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] (A143090)
%e A032451 [17, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [18, 21, 11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [19, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [20, 22, 14, 10, 8, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] (A143733)
%e A032451 [21, 11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [22, 14, 10, 8, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] (A143721)
%e A032451 [23, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [24, 36, 55, 17, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] (A143645)
%e A032451 [25, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, ...]
%e A032451 [26, 16, 15, 9, 4, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] (A143759)
%e A032451 [27, 13, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, ...]
%e A032451 [29, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [30, 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0, 0, 0, 0, 0, 0, ...] (A008885)
%e A032451 [31, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 [32, 31, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A032451 Rows 6, 25 and 28 are omitted from the entry since they never reach 1.
%p A032451 with(numtheory);
%p A032451 f:=proc(n) local i,t1; t1:=[n];
%p A032451 for i from 1 to 20 do t1:=[op(t1), sigma(t1[i])-t1[i]]; od:
%p A032451 t1; end;
%p A032451 for n from 2 through 32 do lprint(f(n)); od:
%K A032451 nonn,tabf
%O A032451 1,2
%A A032451 Ursula Gagelmann (gagelmann(AT)altavista.net)
%E A032451 Edited by _N. J. A. Sloane_, Nov 30 2008