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A232444
Numbers n such that sigma(n) and sigma(n^2) are primes.
4
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
OFFSET
1,1
COMMENTS
Intersection of A023194 and A055638.
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.
LINKS
Donovan Johnson and Chai Wah Wu, Table of n, a(n) for n = 1..10385 [Terms from 1 to 500 from Donovan Johnson]
EXAMPLE
4 is in the sequence because both sigma(4)=7 and sigma(4^2)=31 are primes.
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Nov 24 2013
EXTENSIONS
a(6)-a(12) from Michel Marcus, Nov 26 2013
a(13)-a(29) from Alex Ratushnyak, Nov 26 2013
STATUS
approved