A087269 Nonprime solutions to gcd(x, pi(x)) = gcd(x, A000720(x)) = 1.

1, 9, 12, 18, 21, 25, 26, 28, 32, 34, 35, 36, 42, 45, 49, 52, 55, 57, 60, 65, 68, 69, 70, 74, 76, 81, 84, 85, 86, 87, 88, 91, 95, 98, 99, 104, 106, 110, 111, 112, 119, 121, 128, 129, 130, 133, 135, 141, 143, 145, 147, 155, 158, 159, 160, 161, 162, 165, 170, 172, 177

Offset

1,2

Comments

What is the density of this sequence? - David A. Corneth, Oct 21 2019

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

There are 37 primes below the nonprime 162, so pi(162) = 37 and as gcd(162, pi(162)) = gcd(162, 37) = 1, 162 is in the sequence. - David A. Corneth, Oct 21 2019

Mathematica

t=Table[GCD[w, PrimePi[w]], {w, 1, 1000}]; f=Flatten[Position[t, 1]]; cf=Part[f, Flatten[Position[PrimeQ[f], False]]]

Prog

(PARI) first(n) = {n = max(n, 2); my(q = 2, i = 1, t = 1, res = vector(n)); res[1] = 1; forprime(p = 3, oo, for(j = q + 1, p - 1, if(gcd(t, j) == 1, i++; if(i <= n, res[i] = j; , return(res); ) ) ); t++; q = p ) } \\ David A. Corneth, Oct 21 2019

Crossrefs

Cf. A000720, A007053, A057809, A087266, A087267, A087268.

Sequence in context: A141552 A317720 A162822 * A153973 A072702 A357185

Adjacent sequences: A087266 A087267 A087268 * A087270 A087271 A087272

Keyword

nonn,easy

Author

Labos Elemer, Sep 16 2003

Status

approved