A077064 Squarefree numbers of form prime - 1.

1, 2, 6, 10, 22, 30, 42, 46, 58, 66, 70, 78, 82, 102, 106, 130, 138, 166, 178, 190, 210, 222, 226, 238, 262, 282, 310, 330, 346, 358, 366, 382, 418, 430, 438, 442, 462, 466, 478, 498, 502, 546, 562, 570, 586, 598, 606, 618, 642, 646, 658, 682, 690, 718, 742

Offset

1,2

Comments

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Radoslav Tsvetkov, On the distribution of k-free numbers and r-tuples of k-free numbers. A survey, Notes on Number Theory and Discrete Mathematics, Vol. 25, No. 3 (2019), pp. 207-222. See section 3.4, p. 210.

G. D. Victorovich, On additive property of arithmetic functions (in Russian), Thesis, Moscow State University, 2013.

Example

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

Mathematica

Select[Prime[Range[200]]-1, SquareFreeQ] (* Harvey P. Dale, Feb 09 2015 *)

Prog

(PARI) isok(n) = issquarefree(n) && isprime(n+1); \\ Michel Marcus, Mar 22 2016
(PARI) lista(nn) = forprime(p=2, nn, if (issquarefree(p-1), print1(p-1, ", "))); \\ Michel Marcus, Mar 22 2016

Crossrefs

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

Sequence in context: A180230 A186296 A140775 * A080715 A034168 A055745

Adjacent sequences: A077061 A077062 A077063 * A077065 A077066 A077067

Keyword

nonn

Author

Reinhard Zumkeller, Oct 23 2002

Extensions

Wrong formula removed by Amiram Eldar, Dec 29 2020

Status

approved