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A067350
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Numbers n such that sigma(n)+phi(n) has exactly 4 divisors.
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3
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3, 5, 6, 7, 10, 11, 13, 16, 17, 19, 22, 23, 25, 27, 29, 31, 37, 40, 41, 43, 46, 47, 52, 53, 58, 59, 61, 64, 67, 68, 71, 72, 73, 79, 80, 82, 83, 89, 97, 98, 101, 103, 106, 107, 109, 113, 117, 127, 128, 131, 136, 137, 139, 144, 149, 151, 157, 162, 163, 166, 167, 169
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OFFSET
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1,1
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COMMENTS
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For all terms up to 10^12, sigma(n)+phi(n) is a product of 2 distinct primes. The only other possibility is that sigma(n)+phi(n) is a cube of a prime, for some n which is either a square or twice a square; does this occur? If not, then this sequence is contained in A067351.
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LINKS
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FORMULA
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EXAMPLE
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Includes all odd primes and some composites; e.g. 22 and 25, since sigma(22)+phi(22)=36+10=46=2*23 and sigma(25)+phi(25)=31+20=51=3*17.
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MATHEMATICA
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Select[ Range[ 1, 200 ], DivisorSigma[ 0, DivisorSigma[ 1, # ]+EulerPhi[ # ] ]==4& ]
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PROG
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(PARI) isok(n) = numdiv(sigma(n)+eulerphi(n)) == 4; \\ Michel Marcus, Aug 13 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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