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%I #26 Aug 10 2015 10:48:18
%S 1,2,3,4,5,6,8,9,10,12,13,15,16,18,19,20,24,25,26,30,32,36,38,39,40,
%T 43,45,48,50,52,57,60,64,65,72,73,75,76,78,80,86,90,95,96,100,104,114,
%U 117,120,129,130,144,146,150,152,156,160,171,172,180,181,190
%N Divisors of 7^24 - 1.
%C Number of divisors of k^24-1 for k = 2..10: 96 (2), 384 (3), 768 (4), 1152 (5), 512 (6), 16128 (7), 8192 (8), 14336 (9), 2048 (10).
%C The following 36 triangular numbers belong to this sequence: 1, 3, 6, 10, 15, 36, 45, 78, 120, 171, 190, 300, 325, 741, 780, 2080, 2628, 2850, 4560, 8256, 8385, 14706, 16290, 18528, 74691, 170820, 334153, 450775, 720600, 1664400, 4191960, 5915080, 8654880, 19068400, 1730160900, 23947653922570801800.
%C There are 50 divisors a(k) such that a(k) is divisible by k.
%C Sum( A000005(a(i))^3, i=1..16128 ) = sum( A000005(a(i)), i=1..16128 )^2, see Kordemsky in References and Barbeau et al. in Links section.
%D Boris A. Kordemsky, The Moscow Puzzles: 359 Mathematical Recreations, C. Scribner's Sons (1972), Chapter XIII, Paragraph 349.
%H Michael De Vlieger, <a href="/A245030/b245030.txt">Table of n, a(n) for n = 1..16128</a>
%H Edward Barbeau and Samer Seraj, <a href="http://arxiv.org/abs/1306.5257">Sum of Cubes is Square of Sum</a>, arXiv:1306.5257 [math.NT]
%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>
%e 191581231380566414400 = 2^6*3^2*5^2*13*19*43*73*181*193*409*1201.
%t Divisors[7^24 - 1]
%o (PARI) divisors(7^24-1)
%Y Cf. A000005, A158649, A245027.
%K nonn,fini,full
%O 1,2
%A _Bruno Berselli_, Jul 10 2014
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