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A049097
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Primes p such that p+1 is squarefree.
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17
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2, 5, 13, 29, 37, 41, 61, 73, 101, 109, 113, 137, 157, 173, 181, 193, 229, 257, 277, 281, 313, 317, 353, 373, 389, 397, 401, 409, 421, 433, 457, 461, 509, 541, 569, 601, 613, 617, 641, 653, 661, 673, 677, 709, 733, 757, 761, 769, 797, 821, 829, 853, 857
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OFFSET
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1,1
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COMMENTS
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Numbers k such that core(sigma(k)) = k + 1 where core(k) is the squarefree part of k (A007913). - Benoit Cloitre, May 01 2002
This sequence is infinite and its relative density in the sequence of primes is equal to Artin's constant (A005596): Product_{p prime} (1-1/(p*(p-1)) = 0.373955... (Mirsky, 1949). - Amiram Eldar, Dec 29 2020
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LINKS
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FORMULA
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EXAMPLE
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29 is included since 29 + 1 = 30 = 2*3*5 is squarefree.
17 is not here because 18 is divisible by a square, 9.
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MAPLE
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N:= 10000; # to get all entries up to N
A049097:= select(t -> isprime(t) and numtheory:-issqrfree(t+1), [2, seq(1+2*k, k=1..floor((N-1)/2))]); # Robert Israel, May 11 2014
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MATHEMATICA
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Select[Prime[Range[100]], SquareFreeQ[# + 1] &] (* Zak Seidov, Feb 08 2016 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(900) | IsSquarefree(p+1) ]; // Vincenzo Librandi, Dec 25 2010
(PARI) lista(nn) = forprime(p=1, nn, if (issquarefree(p+1), print1(p, ", "))); \\ Michel Marcus, Jan 08 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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