A073455 -id:A073455 - cp's OEIS frontend

A073457 Numbers k such that phi(k) = pi(k) + 2.

7, 9, 15, 16, 22, 54, 66, 120, 210

Offset: 1

Labos Elemer, Aug 02 2002

Solutions to A000010(x) = A000720(x)+m, where m=+2; finite for any fixed value of m.

			8 primes below 22 = {2,3,5,7,11,13,17,19}; 10 terms in RRS[22]={1,3,5,7,9,13,15,17,19,21}, so 22 is here.

Cf. A037228, A037171, A000010, A000720, A073455, A072456.

[n: n in [2..1000] | EulerPhi(n) eq #PrimesUpTo(n)+2]; // Vincenzo Librandi, May 10 2015

with(numtheory): A073457:=n->`if`(phi(n) = pi(n) + 2, n, NULL): seq(A073457(n), n=1..210); # Wesley Ivan Hurt, May 12 2015

Do[s=EulerPhi[n]-PrimePi[n]; If[Equal[s, 2], Print[n]], {n, 10000}]
Select[Range[250],EulerPhi[#]-PrimePi[#]==2&] (* Harvey P. Dale, Jun 22 2025 *)

A073456 Numbers n such that phi(n) = pi(n)+1.

Original entry on oeis.org

1, 5, 36, 48, 84

Offset: 1

Labos Elemer, Aug 02 2002

			15 primes below 48 = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47}; 16 terms in RRS[48]={1,5,7,11,13,17,19,23,25,29,31,35,37,41,43,47}, so 48 is here.

Cf. A037228, A037171, A000010, A000720, A073455.

Do[s=EulerPhi[n]-PrimePi[n]; If[Equal[s, 1], Print[n]], {n, 1, 10000}]
Select[Range[100],EulerPhi[#]==PrimePi[#]+1&] (* Harvey P. Dale, Oct 23 2024 *)

Solutions to A000010(x)=A000720(x)+k, where k=+1; finite for any fixed value of k.

Definition modified by Harvey P. Dale, Oct 23 2024

A073464 a(n) = phi(n) mod PrimePi(n).

Original entry on oeis.org

0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 6, 2, 0, 4, 2, 4, 8, 2, 3, 0, 3, 8, 8, 8, 5, 9, 5, 2, 1, 0, 6, 0, 4, 1, 12, 0, 6, 10, 8, 1, 1, 12, 5, 2, 9, 4, 2, 8, 8, 4, 12, 7, 16, 6, 12, 0, 14, 12, 2, 9, 13, 6, 5, 10, 4, 9, 15, 19, 15, 18, 3, 12, 10, 10, 18, 13, 1, 18, 19, 10, 17, 16, 0, 0, 20, 12

Offset: 2

Labos Elemer, Aug 02 2002

nonn

Vincenzo Librandi, Table of n, a(n) for n = 2..10000

Cf. A000010, A000720.
Cf. A037228, A037171.
Cf. A073453, A073454, A073455, A073456, A073457, A072530, A072531, A073461, A073461.

[EulerPhi(n) mod #PrimesUpTo(n): n in [2..100]]; // Vincenzo Librandi, Dec 11 2018

a(n)=Table[Mod[EulerPhi[w], PrimePi[w]], {w, 2, 1000}]

a(n) = eulerphi(n) % primepi(n); \\ Michel Marcus, Dec 11 2018

a(n) = A000010(n) mod A000720(n).

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A073457 Numbers k such that phi(k) = pi(k) + 2.

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A073456 Numbers n such that phi(n) = pi(n)+1.

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A073464 a(n) = phi(n) mod PrimePi(n).

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