A045745 Numbers n such that sum of proper divisors s(n) is a triangular number T(k).

1, 2, 3, 4, 5, 6, 7, 11, 13, 14, 16, 17, 18, 19, 23, 24, 25, 28, 29, 31, 33, 36, 37, 41, 43, 47, 51, 53, 54, 59, 61, 66, 67, 71, 73, 79, 83, 89, 91, 97, 101, 103, 107, 109, 112, 113, 123, 127, 131, 135, 137, 139, 149, 151, 157, 163, 167, 172, 173, 179, 181, 191, 193

Offset: 1

Author

Felice Russo

Keywords

• nonn
• easy

Examples

			s(14)=1+2+7=10 is a triangular number. In fact T(4)=10.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217.

Programs

Maple

select(t -> issqr(1+8*(numtheory:-sigma(t)-t)), [$1..1000]); # Robert Israel, Dec 25 2016

Mathematica

tri[ n_ ] := Module[ {}, a=Floor[ N[ Sqrt[ 2n ] ] ]; a(a+1)/2==n ]; Select[ Range[ 300 ], tri[ Apply[ Plus, Divisors[ # ] ]-# ]& ]

Extensions

More terms from Erich Friedman