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

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

1,2

Links

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

Example

14 is a term since s(14) = 1+2+7 = 10 = A000217(4) is a triangular number.

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[ # ] ]-# ]& ]

Prog

(PARI) isok(k) = ispolygonal(sigma(k) - k, 3); \\ Amiram Eldar, Mar 05 2026

Crossrefs

Cf. A000217, A001065, A010054.

Sequence in context: A115037 A280536 A090563 * A054010 A051948 A193461

Adjacent sequences: A045742 A045743 A045744 * A045746 A045747 A045748

Keyword

nonn,easy

Author

Felice Russo

Extensions

More terms from Erich Friedman

Status

approved