A045745 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

EXAMPLE

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

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[ # ] ]-# ]& ]

CROSSREFS