A262613 Sum of divisors of n-th generalized pentagonal number.

1, 3, 6, 8, 28, 24, 36, 42, 48, 90, 72, 80, 144, 96, 168, 217, 182, 312, 180, 192, 372, 216, 576, 456, 280, 588, 336, 352, 864, 576, 720, 855, 558, 756, 702, 936, 1120, 600, 1080, 1116, 1024, 2016, 1008, 816, 1296, 1152, 2016, 2072, 1178, 1860, 1344, 1120, 3600

Offset: 1

Author

Omar E. Pol, Nov 24 2015

Keywords

• nonn
• easy

Comments

For a remarkable connection between the sum-of-divisors function (A000203) and the generalized pentagonal numbers (A001318) see A238442.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000203, A001318, A074285, A117948, A196020, A238442.

Programs

Magma

[DivisorSigma(1,(3*n^2+2*n+(n mod 2)*(2*n+1)) div 8): n in [1..70]]; // Vincenzo Librandi, Dec 21 2015

Mathematica

DivisorSigma[1, Select[Accumulate[Range[200]]/3, IntegerQ]] (* G. C. Greubel, Jun 06 2017 *)

PARI

a(n) = sigma((3*n^2 + 2*n + (n%2) * (2*n + 1)) / 8); \\ Michel Marcus, Dec 21 2015

Scheme

(define (A262613 n) (A000203 (A001318 n))) ;; Scheme-program for A000203 given in that entry.
;; This uses memoization-macro definec:
(definec (A001318 n) (if (zero? n) 0 (+ (if (even? n) (/ n 2) n) (A001318 (- n 1)))))
;; Antti Karttunen, Dec 20 2015

Formula

a(n) = A000203(A001318(n)).

Sum_{k=1..n} a(k) ~ (9/40) * n^3. - Amiram Eldar, Dec 14 2024