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A100713
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Hyperperfect brilliant numbers.
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0
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OFFSET
| 1,1
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REFERENCES
| Guy, R. K. "Almost Perfect, Quasi-Perfect, Pseudoperfect, Harmonic, Weird, Multiperfect and Hyperperfect Numbers." Section B2 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 45-53, 1994.
Minoli, D. "Issues in Nonlinear Hyperperfect Numbers." Math. Comput. 34, 639-645, 1980.
Roberts, J. The Lure of the Integers. Washington, DC: Math. Assoc. Amer., p. 177, 1992.
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LINKS
| McCranie, J. S., A Study of Hyperperfect Numbers. J. Integer Sequences 3, No. 00.1.3, 2000.
Eric Weisstein's World of Mathematics, Hyperperfect Number.
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FORMULA
| a(n) is an element in the intersection of A007592 and A078972. a(n)=m(sigma(a(n))-a(n)-1)+1 for some m>1 and a(n) is a semiprime with the same number of digits in each prime factor.
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EXAMPLE
| 21 = 3 * 7, 697 = 17 * 41, 1333 = 31 * 43, 1909 = 23 * 83, 3901 = 47 * 83, 96361 = 173 * 557, 130153 = 157 * 829, 163201 = 293 * 557.
a(2) = 697 because 697 is a 12-hyperperfect number, A028500(2) and is a brilliant number because 697 = 17 * 41.
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CROSSREFS
| Cf. A007592, A078972, A001358.
Sequence in context: A158216 A020246 A006934 * A056565 A187359 A009167
Adjacent sequences: A100710 A100711 A100712 * A100714 A100715 A100716
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KEYWORD
| easy,nonn,base
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 11 2004
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