A048848 -id:A048848 - cp's OEIS frontend

A048849 a(n) = prime(phi(n)) + phi(prime(n)).

3, 4, 7, 9, 17, 15, 29, 25, 35, 35, 59, 43, 77, 55, 65, 71, 111, 73, 127, 89, 109, 107, 161, 107, 167, 137, 163, 143, 215, 131, 239, 183, 207, 191, 237, 187, 307, 223, 255, 225, 351, 217, 371, 263, 285, 277, 409, 275, 407, 299, 363, 327, 479, 311, 429, 351, 419

Offset: 1

N. J. A. Sloane

I made this up to demonstrate how easy it is to construct dull but unguessable sequences with short descriptions.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A000010, A000040, A048848.

[NthPrime(EulerPhi(n)) + EulerPhi(NthPrime(n)) : n in [1..100]]; // G. C. Greubel, Feb 22 2024

with(numtheory); [ seq(ithprime(phi(i))+phi(ithprime(i)),i=1..80) ];

Table[Prime[EulerPhi[n]] + EulerPhi[Prime[n]], {n,100}] (* G. C. Greubel, Feb 22 2024 *)

[nth_prime(euler_phi(n)) + euler_phi(nth_prime(n)) for n in range(1,101)] # G. C. Greubel, Feb 22 2024

Offset corrected by G. C. Greubel, Feb 22 2024

A103176 Let p = prime(sigma(n)) and q = prime(phi(n)), then p is in the sequence if p-q = 6.

Original entry on oeis.org

13, 19, 43, 113, 463, 619, 863, 1789, 2273, 2383, 4519, 4789, 4937, 5443, 5507, 5653, 8237, 10459, 13007, 13697, 16063, 16453, 17389, 18313, 18919, 20903, 21193, 21319, 21383, 23567, 24109, 25309, 26267, 27947, 28283, 29573, 30559, 31183, 31517

Offset: 1

Labos Elemer, Mar 02 2005

nonn

Conjecture: In all cases sigma(n)-phi(n)=2, i.e., n is prime.

Proof: Suppose n is composite. Then sigma(n) > n + sqrt(n) and phi(n) <= n - sqrt(n) and so prime(sigma(n)) - prime(phi(n)) >= sigma(n) - phi(n) > 2*sqrt(n) > 6 for n > 9. - Charles R Greathouse IV, May 15 2013

			n=3719, sigma(n)=3720, phi(n)=3718, a(n)=p(sigma(n))=34847.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A067161, A048848, A000020, A000203.

Do[g=n;a=Prime[u=DivisorSigma[1,n]]; b=Prime[w=EulerPhi[n]];s=a-b; If[Equal[s,6],Print[{n,a,b,u,w,u-w}]; ta=Append[ta,a]],{n,1,10000}] ta=Delete[ta,1]
Prime[DivisorSigma[1,#]]&/@Select[Range[5000],Prime[DivisorSigma[ 1,#]] == Prime[ EulerPhi[#]]+6&] (* Harvey P. Dale, Sep 22 2016 *)

p=2;q=3;forprime(r=5,1e6,if(r-p==6 && isprime(primepi(q)), print1(r", "));p=q;q=r) \\ Charles R Greathouse IV, May 15 2013

a(1) corrected by Charles R Greathouse IV, May 15 2013

cp's OEIS Frontend

A048849 a(n) = prime(phi(n)) + phi(prime(n)).

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