A007592 Hyperperfect numbers: k = m*(sigma(k) - k - 1) + 1 for some m > 1. (Formerly M5113)

21, 301, 325, 697, 1333, 1909, 2041, 2133, 3901, 10693, 16513, 19521, 24601, 26977, 51301, 96361, 130153, 159841, 163201, 176661, 214273, 250321, 275833, 296341, 306181, 389593, 486877, 495529, 542413, 808861, 1005421, 1005649, 1055833, 1063141, 1232053

Offset

1,1

References

D. Minoli, Sufficient Forms For Generalized Perfect Numbers, Ann. Fac. Sciences, Univ. Nation. Zaire, Section Mathem; Vol. 4, No. 2, Dec 1978, pp. 277-302.

D. Minoli, New Results For Hyperperfect Numbers, Abstracts American Math. Soc., October 1980, Issue 6, Vol. 1, pp. 561.

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

Donovan Johnson, Table of n, a(n) for n = 1..10000

Mariano Garcia, Hyperperfect Numbers with Five and Six Different Prime Factors, Fib. Quart. 42, no. 4, Nov. 2004, pp. 292-294.

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

D. Minoli and Robert Bear, Hyperperfect Numbers, Pi Mu Epsilon Journal, Fall 1975, pp. 153-157.

Daniel Minoli, W. Nakamine, Mersenne Numbers Rooted On 3 For Number Theoretic Transforms, 1980 IEEE International Conf. on Acoust., Speech and Signal Processing.

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

D. Minoli, Structural Issues For Hyperperfect Numbers, Fibonacci Quarterly, Feb. 1981, Vol. 19, No. 1, pp. 6-14.

Herman J. J. te Riele, Hyperperfect numbers with three different prime factors, Math. Comp. 36 (1981), 297-298.

Eric Weisstein's World of Mathematics, Hyperperfect Number.

Mathematica

hpnQ[n_]:=Module[{den=DivisorSigma[1, n]-n-1, c}, If[den!=0, c=(n-1)/den, c=Pi]; IntegerQ[c]&&c>1]; Select[Range[1250000], hpnQ] (* Harvey P. Dale, Aug 11 2012 *)

Crossrefs

See A034897 (for m >= 1).

Sequence in context: A021604 A025935 A077506 * A019664 A019839 A077513

Adjacent sequences: A007589 A007590 A007591 * A007593 A007594 A007595

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from Jud McCranie, Oct 15 1997

Status

approved