

A244448


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


6



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
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OFFSET

0,1


COMMENTS

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(xn) + sigma(x+n) = phi(x+n) + sigma(xn). But for these many solutions x, both numbers xn and x+n are primes.
a(n) is the smallest integer m such that mn is composite and A051612(m+n) = A051612(mn) where A051612(n) = sigma(n)  phi(n).  Michel Marcus, Mar 20 2020


LINKS

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


EXAMPLE

a(1)=153 because 1531 is composite, phi(1531)+sigma(153+1) = phi(153+1)+sigma(1531) and there is no such number less than 153.


MATHEMATICA

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


PROG

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


CROSSREFS

Cf. A000010 (phi), A000203 (sigma), A051612 (sigma  phi).
Cf. A244446, A244447, A246628.
Sequence in context: A264711 A279325 A158104 * A197204 A197802 A229313
Adjacent sequences: A244445 A244446 A244447 * A244449 A244450 A244451


KEYWORD

nonn


AUTHOR

Jahangeer Kholdi and Farideh Firoozbakht, Aug 30 2014


STATUS

approved



