A007594 Smallest n-hyperperfect number: m such that m=n(sigma(m)-m-1)+1; or 0 if no such number exists. (Formerly M4150)

6, 21, 325, 1950625

Offset

1,1

Comments

Jud McCranie reports that the following terms are known:

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

69091933912976476978420033,?,1333,51301,?,?,

865004941741938633917612789573739286076451841,?,?,?,?,?

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

References

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

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

Links

Table of n, a(n) for n=1..4.

J. S. McCranie, A study of hyperperfect numbers, J. Int. Seqs. Vol. 3 (2000) #P00.1.3.

Daniel Minoli, Issues In Non-Linear Hyperperfect Numbers, Mathematics of Computation, Vol. 34, No. 150, April 1980, pp. 639-645.

Crossrefs

Sequence in context: A164643 A190275 A261844 * A316775 A181593 A084539

Adjacent sequences: A007591 A007592 A007593 * A007595 A007596 A007597

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved