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A045745 Numbers n such that sum of proper divisors s(n) is a triangular number T(k). 1
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

Cf. A000217.

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

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Last modified September 20 21:03 EDT 2019. Contains 327247 sequences. (Running on oeis4.)