A109131 Admirable numbers such that the subtracted divisor is a triangular number.

20, 24, 30, 42, 54, 66, 78, 84, 102, 104, 114, 138, 140, 174, 186, 222, 224, 246, 258, 282, 308, 318, 354, 364, 366, 402, 426, 438, 464, 474, 476, 498, 532, 534, 582, 606, 618, 642, 644, 650, 654, 678, 762, 786, 812, 822, 834, 868, 894, 906, 942, 945, 978

Offset: 1

Author

Jason Earls, Aug 17 2005

Keywords

• easy
• nonn

Examples

			a(2)=24 because 1+2+3+4+8+12-6 = 24 and the subtracted divisor is triangular.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217 (triangular numbers), A111592 (admirable numbers).

Programs

Mathematica

triQ[n_] := IntegerQ @ Sqrt[8n + 1]; Select[Range[1000], MemberQ[Divisors[#], (d = (DivisorSigma[1, #] - 2#)/2)] && triQ[d] &] (* Amiram Eldar, Sep 21 2019 *)