A298762 Numbers n such that uphi(n) = uphi(n+2) - uphi(n+1), where uphi is the unitary totient function (A047994).
1, 2, 5, 21, 9177, 244965, 14307854, 24571869, 128199057, 140830365, 401767629, 420567854, 468190437, 525970977, 780768165, 886434645, 1597167645, 4046753949, 4473784821, 5364666165, 5515718205, 11175736334, 14408460165, 18026319710, 20106993885, 20357733129
Offset: 1
Keywords
Examples
21 is in the sequence since uphi(21) = 12 = uphi(23) - uphi(22) = 22 - 10.
Programs
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Mathematica
uphi[n_] := If[n>1,(Times @@ (Table[ #[[1]]^ #[[2]] - 1, {1} ] & /@ FactorInteger[n]))[[1]],1]; Select[Range[10^7], uphi[#] == uphi[# + 2] - uphi[# + 1] &] -
PARI
uphi(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[1, 2]-1); isok(n) = uphi(n) == uphi(n+2) - uphi(n+1); \\ Michel Marcus, Jan 26 2018
Extensions
a(7)-a(26) from Giovanni Resta, Jan 26 2018