A246628 -id:A246628 - cp's OEIS frontend

A246629 a(n) = A244448(A246628(n)).

153, 442, 145416, 174417, 499305, 826312, 1134378, 2452587, 3340976, 3617130, 5141892

Offset: 1

Jahangeer Kholdi and Farideh Firoozbakht, Sep 01 2014

			A244448(A246628(1)) = A244448(1) = 153.
A244448(A246628(2)) = A244448(2) = 442.
A244448(A246628(7)) = A244448(7598) = 1134378.

Cf. A244448, A246628.

a(8)-a(11) from Jinyuan Wang, Mar 18 2020

A244448 a(n) is the smallest integer m such that m-n is composite and phi(m-n) + sigma(m+n) = phi(m+n) + sigma(m-n).

Original entry on oeis.org

4, 153, 442, 213, 179, 120, 46, 37, 47, 264, 145416, 1101, 107, 79, 71, 78, 716, 637, 98, 249, 71, 126, 13258, 1243, 119, 163, 119, 131, 140497, 381, 191, 156, 101, 169, 1574, 315, 151, 193, 167, 2158, 148, 104, 202, 289, 1969, 882, 2572, 428, 251, 357, 314, 283

Offset: 0

Jahangeer Kholdi and Farideh Firoozbakht, Aug 30 2014

nonn

For each n, a(n) > n and like a(n)-n, a(n)+n is also composite.
If both numbers p and p + 2n are primes then x = p+n is a solution to the equation phi(x-n) + sigma(x+n) = phi(x+n) + sigma(x-n). But for these many solutions x, both numbers x-n and x+n are primes.
a(n) is the smallest integer m such that m-n is composite and A051612(m+n) = A051612(m-n) where A051612(n) = sigma(n) - phi(n). - Michel Marcus, Mar 20 2020

			a(1)=153 because 153-1 is composite, phi(153-1)+sigma(153+1) = phi(153+1)+sigma(153-1) and there is no such number less than 153.

Michel Marcus, Table of n, a(n) for n = 0..4501 (terms 0..1000 from Jinyuan Wang)

Cf. A000010 (phi), A000203 (sigma), A051612 (sigma - phi).

Cf. A244446, A244447, A246628.

a[0]=4;a[n_]:=a[n]=(For[m=n+1,PrimeQ[m-n]||EulerPhi[m-n]+DivisorSigma[1,m+n]!=EulerPhi[m+n]+DivisorSigma[1,m-n],m++];m);
Table[a[n],{n,0,70}]

a(n) = {my(m=n+4); while(isprime(m-n) || eulerphi(m+n)+sigma(m-n)!=eulerphi(m-n)+sigma(m+n), m++); m; }
vector(100,n,a(n)) \\ Derek Orr, Aug 30 2014

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A246629 a(n) = A244448(A246628(n)).

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A244448 a(n) is the smallest integer m such that m-n is composite and phi(m-n) + sigma(m+n) = phi(m+n) + sigma(m-n).

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