A232355 Numbers k such that sigma(triangular(k)) = sigma(k)^2.

1, 11, 695, 991, 2839, 3707, 9347, 10703, 12847, 27089, 42251, 56419, 74671, 115289, 168739, 191051, 219295, 233729, 280111, 300731, 326899, 353651, 430859, 611799, 642991, 661715, 1035827, 1116607, 1181579, 1234519, 1365491, 1485035, 1777099, 1854671, 1905875

Offset: 1

Author

Alex Ratushnyak, Nov 22 2013

Keywords

• nonn

Comments

Subsequence of A116990. - Michel Marcus, Jun 13 2015

Examples

			11 is in the sequence because sigma(11*12/2) = sigma(66) = 144 = 12^2 = sigma(11)^2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000203 (sigma(n): sum of divisors of n), A000217 (triangular(n): = n*(n+1)/2).

Cf. A074285 (sigma(triangular(n))), A072861 (sigma(n)^2).

Cf. A116990 (indices of triangular numbers whose sum of divisors is square).

Programs

Magma

[n: n in [1..7*10^5] | SumOfDivisors(n*(n+1) div 2) eq SumOfDivisors(n)^2]; // Vincenzo Librandi, Jun 13 2015

Mathematica

Select[Range@1000000, DivisorSigma[1, #]^2==DivisorSigma[1, (# (# + 1)/2)] &] (* Vincenzo Librandi, Jun 13 2015 *)

PARI

isok(n) = sigma(n)^2 == sigma(n*(n+1)/2); \\ Michel Marcus, Nov 23 2013

Extensions

More terms from Michel Marcus, Nov 23 2013