# [seqfan] n-th number whose sum of divisors is a n-gonal number

Jonathan Post jvospost3 at gmail.com
Sat Sep 25 22:43:13 CEST 2010

```The natural generalization of the below is the array A[k,n] = the n-th
number whose sum of divisors is a k-gonal number.

We know the first few values of the k=3 and k = 4 rows.  The main
diagonal A[n,n] = the n-th number whose sum of divisors is a n-gonal
number, would nicely capture that array's upper left corner. Probably
offset to n>2.

%I A180927
%S A180927 1,2,5,8,22,36,45,54,56,98
%N A180927 Numbers n such that the sum of divisors of n is a triangular number.
%C A180927 This is to A006532 (numbers n such that sum of divisors is
a square) as A000217 triangular numbers is to A000290 squares. 54 and
56 are the smallest pair of numbers whose sum of divisors is the same
triangular number.
%F A180927 A000203(a(n)) is in A000217. sigma(a(n) = k*(k+1)/2 for
some nonnegative integer k. Sum of divisors of a(n) is a triangular
number. sigma_1(a(n)) is a triangular number.
%e A180927 a(1) = 1 because the sum of divisors of 1 is the triangular number 1.
%e A180927 a(2) = 2 because the sum of divisors of 2 is the triangular number 3.
%e A180927 a(3) = 5 because the sum of divisors of 5 is the triangular number 6.
%e A180927 a(4) = 8 because the sum of divisors of 8 is the triangular
number 15.
%e A180927 a(5) = 22 because the sum of divisors of 22 is the
triangular number 36.
%e A180927 a(6) = 36 because the sum of divisors of 36 is the
triangular number 91.
%e A180927 a(7) = 45 because the sum of divisors of 45 is the
triangular number 78.
%Y A180927 Cf. A000203, A000217, A000290, A006532.
%K A180927 easy,more,nonn
%O A180927 1,2
%A A180927 Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 25 2010

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