cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A276678 Number of divisors of the n-th pentagonal number.

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%I A276678 #19 Jul 19 2025 15:47:24
%S A276678 1,2,6,4,4,4,8,6,6,4,10,16,4,4,16,8,6,6,12,8,8,8,8,12,6,8,32,8,4,8,8,
%T A276678 20,12,4,24,12,8,4,16,24,4,16,14,8,12,4,16,32,6,6,24,16,4,16,16,12,16,
%U A276678 4,16,16,8,8,24,12,8,8,18,16,8,16,8,36,4,8,60,8
%N A276678 Number of divisors of the n-th pentagonal number.
%H A276678 Colin Barker, <a href="/A276678/b276678.txt">Table of n, a(n) for n = 1..1000</a>
%F A276678 a(n) = A000005(A000326(n)). - _Omar E. Pol_, Sep 13 2016
%e A276678 a(7) = 8 because the 7th pentagonal number is 70, which has 8 divisors: 1,2,5,7,10,14,35,70.
%t A276678 DivisorSigma[0,PolygonalNumber[5,Range[80]]] (* _Harvey P. Dale_, Jul 19 2025 *)
%o A276678 (PARI)
%o A276678 pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
%o A276678 vector(100, n, numdiv(pg(5,n)))
%Y A276678 Cf. A000005, A000326 (pentagonal numbers).
%Y A276678 Cf. A063440 (m=3), A048691 (m=4), A276679 (m=6), A276680 (m=7), A276681 (m=8), A276682 (m=9), A276683 (m=10).
%K A276678 nonn
%O A276678 1,2
%A A276678 _Colin Barker_, Sep 13 2016