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A055638
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Numbers n for which sigma(n^2) is prime.
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11
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2, 3, 4, 5, 8, 17, 27, 41, 49, 59, 64, 71, 89, 101, 125, 131, 167, 169, 173, 256, 289, 293, 383, 512, 529, 677, 701, 729, 743, 761, 773, 827, 839, 841, 857, 911, 1091, 1097, 1163, 1181, 1193, 1217, 1373, 1427, 1487, 1559, 1583, 1709, 1811, 1847, 1849, 1931
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OFFSET
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1,1
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COMMENTS
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sigma(n) is the sum of the divisors of n (A000203).
If sigma(x) is prime, then x=2 or x=p^(2m), an even power of a prime, cf. A023194. This sequence lists the values n = p^m such that sigma(n^2) is prime, i.e., sqrt( A023194 \ {2} ). The corresponding primes sigma(n^2)=A062700(n) are 1+p+...+p^(2m) = (p^(2m+1)-1)/(p-1), and any prime of that form (cf. A023195) corresponds to a term p^m is in this sequence. - M. F. Hasler, Oct 14 2014
a(n) nearly always has digitsum of the form 1 mod 3. Specifically, 99.8% of the first 33733 entries examined conformed. The first exceptions are 3, 4, 27, 49, 64, 169, 256, 289, 529, 729. The exceptions (examined) appear to be integer powers themselves excepting the initial 3. Similarly, except for the initial 3, all entries of A023195 appear to have digitsum = 1 mod 3. - Bill McEachen, Mar 05 2017
Number of terms < 10^k: 5, 13, 36, 137, 735, 4730, 33732, 253393, ..., . Robert G. Wilson v, Mar 09 2017
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LINKS
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FORMULA
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MATHEMATICA
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Select[Range[2000], PrimeQ[DivisorSigma[1, #^2]] &]
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PROG
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(PARI) for(n=1, 9999, isprime(sigma(n^2))&&print1(n", ")) \\ M. F. Hasler, Oct 18 2014
(Magma) [n: n in [1..2000] | IsPrime(SumOfDivisors(n^2))]; // Vincenzo Librandi, Oct 18 2014
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CROSSREFS
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Cf. A023195 (primes of the form sigma(n)), A062700 (in order of appearance).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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