A100411 Numbers n such that n is the phi(n)-th nonprime number.

1, 4, 8, 27, 35, 215, 235, 2611, 65113, 174647, 1301317, 1302509, 5021647, 10885081, 36319939, 70112131, 70113559, 325575773, 514258883, 742327529, 1069238453, 18721771909, 27788563039, 113350570453, 835005036247

Offset

1,2

Comments

n is in the sequence iff n is't prime and n=phi(n)+pi(n). This sequence is a subsequence of A037170 and 2 is the only term of A037170 which is not in this sequence because 2 is the only prime p such that p=phi(p)+pi(p).

There is no further term up to 10^9. - Farideh Firoozbakht, Jul 26 2009

a(24) > 10^11. - Donovan Johnson, Feb 05 2010

a(26) > 2.3*10^12. - Giovanni Resta, Mar 28 2017

Links

Table of n, a(n) for n=1..25.

Example

27 is in the sequence because phi(27)=18 and 27 is the 18th nonprime number, the first 17 nonprime numbers are 1,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25 & 26.

Mathematica

Select[Range[10^5], # == PrimePi[#] + EulerPhi[#] && ! PrimeQ[#] &] (* Giovanni Resta, Mar 28 2017 *)

Crossrefs

Cf. A037170, A100410, A018252.

Sequence in context: A272228 A051243 A356646 * A065405 A279627 A026085

Adjacent sequences: A100408 A100409 A100410 * A100412 A100413 A100414

Keyword

more,nonn

Author

Farideh Firoozbakht, Dec 01 2004

Extensions

a(19)-a(20) from Farideh Firoozbakht, Jul 26 2009

a(21)-a(23) from Donovan Johnson, Feb 05 2010

a(24)-a(25) from Giovanni Resta, Mar 28 2017

Status

approved