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A049097 Primes p such that p+1 is squarefree. 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

n such that core(sigma(n)) = n + 1 where core(x) is the squarefree part of x. - Benoit Cloitre, May 01 2002

A160696(a(n)) = 1. - Reinhard Zumkeller, May 24 2009

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A077067(n)-1. - Zak Seidov, Mar 19 2016

EXAMPLE

29 is included since 29 + 1 = 30 = 2*3*5 is free of squares; 17 is not here because 18 is divided by a square, 9.

MAPLE

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

MATHEMATICA

Select[Prime[Range[100]], SquareFreeQ[# + 1] &] (* Zak Seidov, Feb 08 2016 *)

PROG

(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

CROSSREFS

Cf. A000040, A005117, A039787.

Cf. A077067.

Sequence in context: A241392 A319778 A002559 * A045366 A158708 A093702

Adjacent sequences:  A049094 A049095 A049096 * A049098 A049099 A049100

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified January 17 20:36 EST 2020. Contains 330987 sequences. (Running on oeis4.)