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A244448
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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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6
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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
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0,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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PROG
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(PARI) 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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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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