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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A009744 A124592 A275203 * A088079 A118993 A219735
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

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Last modified July 19 00:30 EDT 2024. Contains 374388 sequences. (Running on oeis4.)