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A074770
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Numbers n such that tau(n) > tau(n+1), phi(n) > phi(n+1) and sigma(n) > sigma(n+1).
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1
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45, 117, 225, 273, 297, 345, 357, 405, 465, 513, 561, 621, 693, 705, 765, 777, 825, 837, 861, 885, 945, 1005, 1113, 1125, 1185, 1197, 1281, 1305, 1395, 1425, 1521, 1545, 1593, 1617, 1701, 1725, 1845, 1881, 1905, 1953, 1965, 2025, 2037, 2121, 2277
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OFFSET
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1,1
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LINKS
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FORMULA
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It seems that a(n) is asymptotic to c*n with 52 < c < 54.
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EXAMPLE
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tau(117) = 6 > 4 = tau(118), phi(117) = 72 > 58 = phi(118), and sigma(117) = 182 > 180 = sigma(118); hence 117 is in the sequence.
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MAPLE
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N:= 200: # to get the first N terms
prev:= [numtheory:-tau, numtheory:-phi, numtheory:-sigma](1):
count:= 0:
for n from 2 while count < N do
tps:= [numtheory:-tau, numtheory:-phi, numtheory:-sigma](n);
if min(prev - tps) > 0 then count:= count+1; A[count]:= n-1 fi;
prev:= tps;
od:
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MATHEMATICA
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Select[Range[1, 3000], DivisorSigma[0, #] > DivisorSigma[0, #+1] && EulerPhi[#] > EulerPhi[#+1] && DivisorSigma[1, #] > DivisorSigma[1, #+1]&] (* Vaclav Kotesovec, Feb 16 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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STATUS
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approved
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