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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 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

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