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

1,1

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

Cf. A000203, A023194, A055638.

Sequence in context: A009744 A124592 A275203 * A088079 A118993 A219735

Adjacent sequences: A232441 A232442 A232443 * A232445 A232446 A232447

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