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A007592 Hyperperfect numbers: k = m*(sigma(k) - k - 1) + 1 for some m > 1.
(Formerly M5113)
6
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from Jud McCranie, Oct 15 1997
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)