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A075398
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Perfect powers pp such that pp-1 is prime.
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8
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4, 8, 32, 128, 8192, 131072, 524288, 2147483648, 2305843009213693952, 618970019642690137449562112, 162259276829213363391578010288128, 170141183460469231731687303715884105728
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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 (mymontain(AT)yahoo.com), 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
| O. E. Pol, Determinacion geometrica de los numeros primos y perfectos".
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FORMULA
| 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
A075398(n)=(1+Sqrt[1+8*A000396(n)])/2 [From Artur Jasinski (grafix(AT)csl.pl), Sep 23 2008]
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MATHEMATICA
| Select[Table[2^n, {n, 0, 6!}], PrimeQ[ #-1]&] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), May 14 2010]
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CROSSREFS
| Equals Mersenne primes (A000668) + 1.
Cf. A000043.
Cf. A019279, A061652, A129096, A129306.
Sequence in context: A113479 A103970 A034785 * A072868 A098579 A032467
Adjacent sequences: A075395 A075396 A075397 * A075399 A075400 A075401
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KEYWORD
| easy,nonn
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Oct 11 2002
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