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A305656
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Integers m that satisfy tau(m) + omega(m) = #({phi(x) = m}).
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2
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2, 4, 8, 16, 24, 32, 64, 128, 256, 320, 512, 1024, 2048, 3712, 4096, 7168, 8192, 10512, 16192, 16384, 32768, 33024, 37888, 41728, 49280, 51552, 54528, 57280, 62592, 65536, 66432, 67968, 68832, 69792, 81600, 84352, 87696, 91968, 92016, 93888, 94720, 124128, 129888, 131072
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OFFSET
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1,1
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COMMENTS
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All even terms of A000079 are contained in this sequence.
a(5) = 24 is the first term not a term of A000079, a(10) = 320 is the second.
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LINKS
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FORMULA
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tau(m) + omega(m) = #({phi(x) = m}).
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EXAMPLE
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2 is a term because tau(2) = 2, omega(2) = 1, and #({phi(x) = 2}) = 3.
24 is a term because tau(24) = 8, omega(24) = 2, and #({phi(x) = 24}) = 10.
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MAPLE
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filter:= proc(n) uses numtheory; tau(n)+nops(factorset(n)) = nops(invphi(n)) end proc:
select(filter, [seq(i, i=2..10^5, 2)]); # Robert Israel, Oct 28 2021
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MATHEMATICA
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Block[{nn = 10^5, s}, s = Function[s, Function[t, Take[#, nn] &@ ReplacePart[t, Map[# -> Length@ Lookup[s, #] &, Keys@ s]]]@ ConstantArray[0, Max@ Keys@ s]]@ KeySort@ PositionIndex@ Array[EulerPhi, Floor[nn^(3/2)] + 10]; Select[Range@ nn, DivisorSigma[0, #] + PrimeNu[#] == s[[#]] &] ] (* Michael De Vlieger, Jul 21 2018 *)
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PROG
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(PARI) isok(m) = numdiv(m) + omega(m) == #invphi(m); \\ Michel Marcus, Jun 08 2018
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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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