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 A055638 Numbers n for which sigma(n^2) is prime. 9
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 This is a subsequence of A000961, see A248963 for its complement therein. - M. F. Hasler, Oct 19 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 Primes in the sequence are A053182. - Thomas Ordowski, Nov 18 2017 LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 4730 terms from T. D. Noe) FORMULA a(n) = sqrt(A023194(n+1)). Equal to A000961 \ A248963. - M. F. Hasler, Oct 19 2014 MATHEMATICA Select[Range[2000], PrimeQ[DivisorSigma[1, #^2]] &] PROG (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 CROSSREFS Cf. A023194 (sigma(n) is prime). Cf. A023195 (primes of the form sigma(n)), A062700 (in order of appearance). Cf. A000961, A248963. Sequence in context: A264011 A337280 A081711 * A057657 A293591 A116657 Adjacent sequences:  A055635 A055636 A055637 * A055639 A055640 A055641 KEYWORD nonn AUTHOR Robert G. Wilson v, Jun 07 2000 EXTENSIONS Minor edits by M. F. Hasler, Oct 18 2014 STATUS approved

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Last modified April 19 09:52 EDT 2021. Contains 343110 sequences. (Running on oeis4.)