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Search: id:A075398
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| A075398 |
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Perfect powers pp such that pp-1 is prime. |
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+0
8
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| 4, 8, 32, 128, 8192, 131072, 524288, 2147483648, 2305843009213693952, 618970019642690137449562112, 162259276829213363391578010288128, 170141183460469231731687303715884105728
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If n is in the sequence then n is a solution of the equation sigma(sigma(x)-x)=x (*). Because if 2^p-1 is prime and n=2^p then sigma(sigma(n)-n)=sigma((2^(p+1)-1)-2^p)=sigma(2^p-1)=2^p=n. Is it true that there is no other solution for (*)? - Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Dec 05 2005
Twice even superperfect numbers (cf. A061652). Also twice superperfect numbers, if there are no odd superperfect numbers (cf. A019279). Difference between n-th ultraperfect number and n-th infraperfect number. - Omar E. Pol (info(AT)polprimos.com), Apr 25 2008
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LINKS
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O. E. Pol, Determinacion geometrica de los numeros primos y perfectos".
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FORMULA
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a(n) = 2^A000043(n). - Omar E. Pol (info(AT)polprimos.com), Apr 11 2008
a(n) = A139306(n) - A139096(n). a(n) = 2*A061652(n). Also a(n) = 2*A019279(n) if there are no odd superperfect numbers. - Omar E. Pol (info(AT)polprimos.com), Apr 25 2008
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CROSSREFS
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Equals Mersenne primes (A000668) + 1.
Cf. A000043.
Cf. A019279, A061652, A129096, A129306.
Sequence in context: A113479 A103970 A034785 this_sequence A072868 A098579 A032467
Adjacent sequences: A075395 A075396 A075397 this_sequence A075399 A075400 A075401
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KEYWORD
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easy,nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Oct 11 2002
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