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Number of divisors of the n-th pentagonal number.
6

%I #17 Sep 14 2016 04:32:19

%S 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 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 4,16,16,8,8,24,12,8,8,18,16,8,16,8,36,4,8,60,8

%N Number of divisors of the n-th pentagonal number.

%H Colin Barker, <a href="/A276678/b276678.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A000005(A000326(n)). - _Omar E. Pol_, Sep 13 2016

%e a(7) = 8 because the 7th pentagonal number is 70, which has 8 divisors: 1,2,5,7,10,14,35,70.

%o (PARI)

%o pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number

%o vector(100, n, numdiv(pg(5,n)))

%Y Cf. A000005, A000326 (pentagonal numbers).

%Y Cf. A063440 (m=3), A048691 (m=4), A276679 (m=6), A276680 (m=7), A276681 (m=8), A276682 (m=9), A276683 (m=10).

%K nonn

%O 1,2

%A _Colin Barker_, Sep 13 2016