A145199 Nonsquarefree numbers k such that k+1 is prime.

4, 12, 16, 18, 28, 36, 40, 52, 60, 72, 88, 96, 100, 108, 112, 126, 136, 148, 150, 156, 162, 172, 180, 192, 196, 198, 228, 232, 240, 250, 256, 268, 270, 276, 280, 292, 306, 312, 316, 336, 348, 352, 372, 378, 388, 396, 400, 408, 420, 432, 448, 456, 460, 486, 490

Offset: 1

Author

Giovanni Teofilatto, Oct 04 2008

Keywords

• easy
• nonn

Examples

			4 is in the sequence because it is not squarefree and 5 is prime. - _Emeric Deutsch_, Oct 12 2008
		

Links

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

Crossrefs

Cf. A006093, A013929, A049092, A077064. Includes A152680.

Programs

Magma

[n: n in [1..5*10^2]| not IsSquarefree(n) and IsPrime(n+1)]; // Vincenzo Librandi, Dec 24 2015

Maple

with(numtheory): a:=proc(n) if issqrfree(n)=false and isprime(n+1)=true then n else end if end proc: seq(a(n),n=1..600); # Emeric Deutsch, Oct 12 2008
with(numtheory): a:=proc(k) if issqrfree(ithprime(k)-1)=false then ithprime(k)-1 else end if end proc: seq(a(k),k=1..110); # Emeric Deutsch, Oct 12 2008

Mathematica

Select[Prime[Range[120]]-1, !SquareFreeQ[ # ]&] (* T. D. Noe, Oct 06 2008 *)

PARI

is(n)=isprime(n+1) && !issquarefree(n) \\ Charles R Greathouse IV, Jun 13 2017

Formula

a(n) = A049092(n) - 1. - Amiram Eldar, Feb 10 2021

Extensions

Corrected and extended by T. D. Noe, Emeric Deutsch and R. J. Mathar, Oct 05 2008