A077064 - OEIS

%I #38 Aug 22 2024 02:04:40

%S 1,2,6,10,22,30,42,46,58,66,70,78,82,102,106,130,138,166,178,190,210,

%T 222,226,238,262,282,310,330,346,358,366,382,418,430,438,442,462,466,

%U 478,498,502,546,562,570,586,598,606,618,642,646,658,682,690,718,742

%N Squarefree numbers of form prime - 1.

%C 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... (Victorovich, 2013). - _Amiram Eldar_, Dec 29 2020

%H Harvey P. Dale, <a href="/A077064/b077064.txt">Table of n, a(n) for n = 1..10000</a>

%H Radoslav Tsvetkov, <a href="http://doi.org/10.7546/nntdm.2019.25.3.207-222">On the distribution of k-free numbers and r-tuples of k-free numbers. A survey</a>, Notes on Number Theory and Discrete Mathematics, Vol. 25, No. 3 (2019), pp. 207-222. See section 3.4, p. 210.

%H G. D. Victorovich, <a href="https://www.dissercat.com/content/ob-additivnykh-svoistvakh-arifmeticheskikh-funktsii">On additive property of arithmetic functions</a> (in Russian), Thesis, Moscow State University, 2013.

%e A005117(44) = 70 = 2*5*7 is a term as 70 = A000040(20)-1 = 71-1.

%t Select[Prime[Range[200]]-1,SquareFreeQ] (* _Harvey P. Dale_, Feb 09 2015 *)

%o (PARI) isok(n) = issquarefree(n) && isprime(n+1); \\ _Michel Marcus_, Mar 22 2016

%o (PARI) lista(nn) = forprime(p=2, nn, if (issquarefree(p-1), print1(p-1, ", "))); \\ _Michel Marcus_, Mar 22 2016

%Y Cf. A005596, A006093, A005117, A000040, A077063, A077067.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Oct 23 2002

%E Wrong formula removed by _Amiram Eldar_, Dec 29 2020