A281993 Integers m such that sigma(m) + sigma(2*m) = 6*m.

10, 44, 184, 752, 12224, 49024, 12580864, 206158168064, 885443715520878608384, 226673591177468092350464, 232113757366000005450563584, 3894222643901120685369075227951104, 1020847100762815390371677078221595082752, 17126972312471518572699356075530215722269540352

Offset: 1

Author

Michel Marcus, Feb 04 2017

Keywords

• nonn

Comments

This is the case h = 2 of the h-perfect numbers as defined in the Harborth link.

Examples

			10 is a term since sigma(10) + sigma(20) = 60, that is 6*10.
		

Links

• Heiko Harborth, On h-perfect numbers, Annales Mathematicae et Informaticae, 41 (2013) pp. 57-62.

Crossrefs

Cf. A000203, A097215.

Programs

Mathematica

Select[Range[10^7], DivisorSigma[1, #] + DivisorSigma[1, 2 #] == 6 # &] (* Michael De Vlieger, Feb 04 2017 *)

PARI

isok(n, h=2) = sigma(n) + sigma(h*n) == 2*n*(h+1);

Formula

a(n) = 2^A002235(n+1) * A007505(n+1). - Daniel Suteu, Feb 08 2017 [See Harborth link for a proof.]

Extensions

More terms from Jinyuan Wang, Feb 11 2020