A262613 - OEIS

%I #35 Dec 15 2024 07:26:17

%S 1,3,6,8,28,24,36,42,48,90,72,80,144,96,168,217,182,312,180,192,372,

%T 216,576,456,280,588,336,352,864,576,720,855,558,756,702,936,1120,600,

%U 1080,1116,1024,2016,1008,816,1296,1152,2016,2072,1178,1860,1344,1120,3600

%N Sum of divisors of n-th generalized pentagonal number.

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

%H Antti Karttunen, <a href="/A262613/b262613.txt">Table of n, a(n) for n = 1..5000</a>

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

%F Sum_{k=1..n} a(k) ~ (9/40) * n^3. - _Amiram Eldar_, Dec 14 2024

%t DivisorSigma[1, Select[Accumulate[Range[200]]/3, IntegerQ]] (* _G. C. Greubel_, Jun 06 2017 *)

%o (Scheme)

%o (define (A262613 n) (A000203 (A001318 n))) ;; Scheme-program for A000203 given in that entry.

%o ;; This uses memoization-macro definec:

%o (definec (A001318 n) (if (zero? n) 0 (+ (if (even? n) (/ n 2) n) (A001318 (- n 1)))))

%o ;; _Antti Karttunen_, Dec 20 2015

%o (PARI) a(n) = sigma((3*n^2 + 2*n + (n%2) * (2*n + 1)) / 8); \\ _Michel Marcus_, Dec 21 2015

%o (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

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

%K nonn,easy

%O 1,2

%A _Omar E. Pol_, Nov 24 2015