The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A253849 Numbers n such that 2^sigma(n) - 1 is a prime. 3
 2, 4, 9, 16, 25, 64 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also numbers n such that sigma(n) is in A000043, i.e., p = 2^sigma(n) - 1 is a Mersenne prime (A000668). The sequence of corresponding primes p reads: 7, 127, 8191, 2147483647, 2147483647, 170141183460469231731687303715884105727, ..., see A253851. Subsequence of A023194 (numbers n such that sigma(n) is a prime), see there for an explanation why all terms except the first one are squares. The sequence of values of sigma(a(n)) is 3, 7, 13, 31, 31, 127, ... and each term of this sequence must be a prime from the sequence of Mersenne exponents (A000043). See A253850. Sequence differs from A023194 because A023194(7) = 289 but if a(7) exists, it must be a number n such that sigma(n) > A000043(43) = 30402457. a(n) must be an even power of a prime. If it is the square of an odd prime, then this prime must be in A053182. If a(n) is an even power of 2, a(n)=2^(2k), then sigma(a(n))=2^(2k+1)-1. Thus, 2k+1 must be a double Mersenne prime exponent, i.e., such that the corresponding Mersenne prime is again a Mersenne exponent, cf. A103901. Only 4 such primes are known, and a(6)=2^6 (k=3) corresponds to the largest known prime of this type, 2^(2k+1)-1 = 127. - M. F. Hasler, Jan 21 2015 LINKS Table of n, a(n) for n=1..6. EXAMPLE 4 is in the sequence because 2^sigma(4)-1 = 2^7-1 = 127 is prime. MATHEMATICA a253849[n_] := Select[Range@ n, PrimeQ[2^DivisorSigma[1, #] - 1] &]; a253849[20000] (* Michael De Vlieger, Jan 19 2015 *) PROG (Magma) [n: n in[1..10000] | IsPrime((2^SumOfDivisors(n)) - 1)] CROSSREFS Cf. A000043, A000203, A000668, A023194, A023195, A253850, A253851. Sequence in context: A073858 A006474 A110878 * A364131 A077137 A023194 Adjacent sequences: A253846 A253847 A253848 * A253850 A253851 A253852 KEYWORD nonn,more AUTHOR Jaroslav Krizek, Jan 16 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 20 05:29 EDT 2024. Contains 373512 sequences. (Running on oeis4.)