A245030 Divisors of 7^24 - 1.

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, 43, 45, 48, 50, 52, 57, 60, 64, 65, 72, 73, 75, 76, 78, 80, 86, 90, 95, 96, 100, 104, 114, 117, 120, 129, 130, 144, 146, 150, 152, 156, 160, 171, 172, 180, 181, 190

Offset: 1

Author

Bruno Berselli, Jul 10 2014

Keywords

• nonn
• fini
• full

Comments

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).

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.

There are 50 divisors a(k) such that a(k) is divisible by k.

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.

Examples

			191581231380566414400 = 2^6*3^2*5^2*13*19*43*73*181*193*409*1201.
		

References

• Boris A. Kordemsky, The Moscow Puzzles: 359 Mathematical Recreations, C. Scribner's Sons (1972), Chapter XIII, Paragraph 349.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..16128
• Edward Barbeau and Samer Seraj, Sum of Cubes is Square of Sum, arXiv:1306.5257 [math.NT]
• Index entries for sequences related to divisors of numbers

Crossrefs

Cf. A000005, A158649, A245027.

Programs

Mathematica

Divisors[7^24 - 1]

PARI

divisors(7^24-1)