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A197112
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Numbers k such that phi(k) = phi(k+1) + phi(k+2).
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2
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193, 3529, 9337, 27229, 46793, 78181, 90193, 112993, 135013, 437183, 849403, 935219, 1078579, 1283599, 1986973, 2209583, 2341183, 2411173, 2689693, 2744143, 3619069, 3712543, 4738183, 5132983, 6596119, 7829029, 8184713
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OFFSET
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1,1
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COMMENTS
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For k less than 4*10^6, k is prime, semiprime, or triprime (3-almost prime).
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LINKS
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FORMULA
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EXAMPLE
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112993 is in the sequence, because phi(112993) = 106704, phi(112994) = 48384, phi(112995) = 58320 and 106704 = 48384 + 58320.
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MAPLE
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for k from 0 do
if numtheory[phi](k) = numtheory[phi](k+1)+numtheory[phi](k+2) then
printf("%d\n", k) ;
end if;
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MATHEMATICA
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Select[Range[10^5], EulerPhi[#] == EulerPhi[# + 1] + EulerPhi[# + 2] &] (* Alonso del Arte, Oct 13 2011 *)
Position[Partition[EulerPhi[Range[82*10^5]], 3, 1], _?(#[[1]]==#[[2]]+#[[3]]&), 1, Heads->False]//Flatten (* Harvey P. Dale, May 10 2022 *)
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PROG
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(PARI) isok(n) = eulerphi(n) == eulerphi(n+1) + eulerphi(n+2); \\ Michel Marcus, May 15 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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EXTENSIONS
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STATUS
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approved
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