A280097 Sum of the divisors of 24*n - 1.

24, 48, 72, 120, 144, 168, 168, 192, 264, 240, 264, 336, 312, 408, 360, 384, 456, 432, 672, 480, 504, 576, 600, 744, 600, 720, 648, 744, 840, 720, 744, 840, 912, 984, 840, 864, 888, 912, 1296, 1104, 984, 1080, 1032, 1272, 1176, 1104, 1368, 1152, 1488, 1320, 1224, 1320, 1344, 1824, 1320

Offset: 1

Author

Omar E. Pol, Dec 25 2016

Keywords

• nonn
• easy

Comments

All terms are multiples of 24 [Gupta, Sierpinski]. - Vincenzo Librandi, Apr 07 2011

Note that 24n - 1 is also the denominator of the Bruinier-Ono finite algebraic formula for the number of partitions of n (Cf. A183010).

Examples

			For n = 5 we have that 24*5 - 1 = 119, and the sum of the divisors of 119 is 1 + 7 + 17 + 119 = 144, so a(5) = 144.
		

Links

• Hansraj Gupta, Congruent properties of sigma(n), Math. Student 13 (1945), 25-29; entire issue.
• Wacław Sierpiński, Elementary Theory of numbers, Monografie Mathematyczne, Vol. 42 (1964), chapter 4, p. 168.

Crossrefs

Cf. A000203, A008606, A183010, A280098.

Programs

Mathematica

DivisorSigma[1,24*Range[60]-1] (* Harvey P. Dale, Jan 25 2024 *)

PARI

a(n) = sigma(24*n - 1); \\ Amiram Eldar, Jan 09 2025

Formula

a(n) = A000203(A183010(n)).

Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = 4*Pi^2/3 = 13.159472... . - Amiram Eldar, Mar 28 2024