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

1,1

Comments

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

Links

Table of n, a(n) for n=1..14.

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000203, A097215.

Sequence in context: A097416 A076373 A097215 * A126397 A164607 A200189

Adjacent sequences: A281990 A281991 A281992 * A281994 A281995 A281996

Keyword

nonn

Author

Michel Marcus, Feb 04 2017

Extensions

More terms from Jinyuan Wang, Feb 11 2020

Status

approved