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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). 5
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, 2327, 1281, 199, 130, 212, 1128, 148, 1039, 235, 5081, 17483, 271, 430, 257, 431, 1225, 191, 234, 19638 (list; graph; refs; listen; history; text; internal format)
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(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.

LINKS

Table of n, a(n) for n=0..70.

EXAMPLE

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.

MATHEMATICA

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}]

PROG

(PARI)

a(n)=(n)->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

CROSSREFS

Cf. A000010, A000203, A244446, A244447.

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

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Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)