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A232444
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Numbers n such that sigma(n) and sigma(n^2) are primes.
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4
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2, 4, 64, 289, 729, 15625, 7091569, 7778521, 11607649, 15912121, 43546801, 56957209, 138980521, 143688169, 171845881, 210801361, 211673401, 253541929, 256224049, 275792449, 308810329, 329386201, 357172201, 408807961, 499477801, 531625249, 769341169, 1073741824, 1260747049
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OFFSET
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1,1
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COMMENTS
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Sigma(n) = A000203(n) = sum of divisors of n.
Terms a(2)...a(29) are squares of 2, 8, 17, 27, 125, 2663, 2789, 3407, 3989, 6599, 7547, 11789, 11987, 13109, 14519, 14549, 15923, 16007, 16607, 17573, 18149, 18899, 20219, 22349, 23057, 27737, 32768, 35507.
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LINKS
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EXAMPLE
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4 is in the sequence because both sigma(4)=7 and sigma(4^2)=31 are primes.
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PROG
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(PARI) isok(n) = isprime(sigma(n)) && isprime(sigma(n^2)); \\ Michel Marcus, Nov 26 2013
(Python)
from sympy import isprime, divisor_sigma
A232444_list = [2]+[n for n in (d**2 for d in range(1, 10**4)) if isprime(divisor_sigma(n)) and isprime(divisor_sigma(n**2))] # Chai Wah Wu, Jul 23 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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