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A262613
Sum of divisors of n-th generalized pentagonal number.
1
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
1,2
COMMENTS
For a remarkable connection between the sum-of-divisors function (A000203) and the generalized pentagonal numbers (A001318) see A238442.
LINKS
FORMULA
a(n) = A000203(A001318(n)).
MATHEMATICA
DivisorSigma[1, Select[Accumulate[Range[200]]/3, IntegerQ]] (* G. C. Greubel, Jun 06 2017 *)
PROG
(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
(PARI) a(n) = sigma((3*n^2 + 2*n + (n%2) * (2*n + 1)) / 8); \\ Michel Marcus, Dec 21 2015
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Nov 24 2015
STATUS
approved