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Smallest n-hyperperfect number: m such that m=n(sigma(m)-m-1)+1; or 0 if no such number exists.
(Formerly M4150)
0

%I M4150 #18 Mar 12 2016 12:35:39

%S 6,21,325,1950625

%N Smallest n-hyperperfect number: m such that m=n(sigma(m)-m-1)+1; or 0 if no such number exists.

%C _Jud McCranie_ reports that the following terms are known:

%C 6,21,325,1950625,?,301,?,?,?,159841,10693,697,?,?,?,

%C 69091933912976476978420033,?,1333,51301,?,?,

%C 865004941741938633917612789573739286076451841,?,?,?,?,?

%C where the missing terms, if they exist, are > 10^11. The large terms for 16 and 22 are the smallest known (7/98).

%D J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 177.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H J. S. McCranie, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html">A study of hyperperfect numbers</a>, J. Int. Seqs. Vol. 3 (2000) #P00.1.3.

%H Daniel Minoli, <a href="http://dx.doi.org/10.1090/S0025-5718-1980-0559206-9">Issues In Non-Linear Hyperperfect Numbers</a>, Mathematics of Computation, Vol. 34, No. 150, April 1980, pp. 639-645.

%K nonn

%O 1,1

%A _N. J. A. Sloane_.