A232444 Numbers n such that sigma(n) and sigma(n^2) are primes.

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

Author

Alex Ratushnyak, Nov 24 2013

Keywords

• nonn

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.

Examples

			4 is in the sequence because both sigma(4)=7 and sigma(4^2)=31 are primes.
		

Links

• Donovan Johnson and Chai Wah Wu, Table of n, a(n) for n = 1..10385 [Terms from 1 to 500 from Donovan Johnson]

Crossrefs

Cf. A000203, A023194, A055638.

Programs

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

Extensions

a(6)-a(12) from Michel Marcus, Nov 26 2013

a(13)-a(29) from Alex Ratushnyak, Nov 26 2013