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superper
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There are 8 letters in SUPERPER ( E1P3R1S1U1 )
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Definitions of superper in various dictionaries:
SUPERPER - In mathematics, a superperfect number is a positive integer n that satisfies σ 2 ...
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In mathematics, a superperfect number is a positive integer n that satisfies* * * * * σ * * 2 * * * ( * n * ) * = * σ * ( * σ * ( * n * ) * ) * = * 2 * n * * , * * * {\displaystyle \sigma ^{2}(n)=\sigma (\sigma (n))=2n\,,} * where σ is the divisor summatory function. Superperfect numbers are a generalization of perfect numbers. The term was coined by Suryanarayana (1969).The first few superperfect numbers are * * 2, 4, 16, 64, 4096, 65536, 262144, 1073741824, ... (sequence A019279 in the OEIS).To illustrate: it can be seen that 16 is a superperfect number as σ(16) = 1 + 2 + 4 + 8 + 16 = 31, and σ(31) = 1 + 31 = 32, thus σ(σ(16)) = 32 = 2 × 16. * If n is an even superperfect number, then n must be a power of 2, 2k, such that 2k+1 − 1 is a Mersenne prime.It is not known whether there are any odd superperfect numbers. An odd superperfect number n would have to be a square number such that either n or σ(n) is divisible by at least three distinct primes. There are no odd superperfect numbers below 7×1024. |