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A271550
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Numbers n such that n is a squarefree semiprime (i.e., omega(n) = 2 = Omega(n)) and phi(n) + 1 is a prime.
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1
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6, 10, 14, 21, 22, 26, 34, 38, 46, 55, 57, 58, 62, 74, 77, 82, 86, 91, 93, 94, 95, 106, 111, 115, 118, 119, 122, 133, 134, 142, 145, 146, 158, 166, 178, 194, 202, 206, 209, 214, 217, 218, 221, 226, 237, 254, 262, 274, 278, 287, 291, 295, 298, 302, 305, 314, 319, 326, 329
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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21 is in the sequence, because 21 = 3*7 is a semiprime with omega(21) = 2 and phi(21) + 1 = 2*6 + 1 = 13 is a prime.
55 is in the sequence, because 55 = 5*11 is a semiprime with omega(55) = 2 and phi(55) + 1 = 4*10 + 1 = 41 is a prime.
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MATHEMATICA
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Select[Range[400], SquareFreeQ[#]&&PrimeOmega[#]==2&&PrimeQ[EulerPhi[ #]+ 1]&] (* Harvey P. Dale, Aug 08 2020 *)
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PROG
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(PARI) is(n)=my(f=factor(n)); f[, 2]==[1, 1]~ && isprime((f[1, 1]-1)*(f[2, 1]-1)+1) \\ Charles R Greathouse IV, Jul 21 2016
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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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