1,2

sigma(n)/n is in A054030.

Also numbers such that the sum of the reciprocals of the divisors is an integer. - Harvey P. Dale (hpd1(AT)nyu.edu), Jul 24 2001

Luca's solution of problem 11090, which proves that for k>1 there are an infinite number of n such that n divides sigma_k(n), does not apply to this sequence. However, it is conjectured that this sequence is also infinite. - T. D. Noe, Nov 04 2007

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 22.

J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 176.

D. Wells The Penguin Dictionary of Curious and Interesting Numbers, pp. 135-6, Penguin Books 1987.

I. Stewart, L'univers des nombres, "Les nombres multiparfaits", Chapter 15, pp. 82-88, Belin-Pour La Science, Paris 2000.

Florian Luca, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113 (2006), 372-373.

T. D. Noe, Table of n, a(n) for n=1..1600 (using Flammenkamp's data)

Achim Flammenkamp, The Multiply Perfect Numbers Page

Anonymous, Multiply Perfect Numbers

Eric Weisstein's World of Mathematics, Abundancy

Eric Weisstein's World of Mathematics, Hyperperfect Number.

120 is OK because divisors of 120 are {1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, the sum of which is 360=120*3.

Do[ If[ Mod[ DivisorSigma[1, n], n ] == 0, Print[n] ], {n, 2, 2*10^11} ]

Transpose[ Select[ Table[ {n, DivisorSigma[ -1, n ]}, {n, 100000} ], IntegerQ[ # [[ 2 ] ] ]& ] ][[ 1 ] ]

Complement is A054027. Cf. A000203, A054024, A054030.

Cf. A000396, A005820, A027687, A046060, A046061

Sequence in context: A055715 A026031 A002694 this_sequence A065997 A006516 A037131

Adjacent sequences: A007688 A007689 A007690 this_sequence A007692 A007693 A007694

nonn,nice

njas, Robert G. Wilson v (rgwv(AT)rgwv.com)

More terms from Jud Mccranie (j.mccranie(AT)comcast.net) and then from David W. Wilson (davidwwilson(AT)comcast.net).