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A216920
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m such that the integer part of sigma(m)/phi(m) is not attained by any integer less than m.
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0
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1, 2, 3, 6, 10, 12, 20, 30, 42, 60, 120, 210, 420, 630, 840, 2520, 9240, 10080, 27720, 55440, 120120, 360360, 720720, 2162160, 6126120, 12252240, 36756720, 116396280, 232792560, 698377680, 2677114440, 5354228880, 26771144400, 155272637520, 465817912560
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OFFSET
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1,2
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COMMENTS
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For large n we expect the inclusion n <= sigma(a(n))/phi(a(n)) <= n+1.
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LINKS
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EXAMPLE
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a(22) = 360360 is in this list because sigma(360360)/phi(360360) = 22.75 and floor(sigma(k)/phi(k)) != 22 for all k < 360360.
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MAPLE
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local p, q, P, R; with(numtheory):
P := {}; R := NULL; p := 1;
while p < searchlimit do
q := iquo(sigma(p), phi(p));
if not member(q, P) then
P := {q} union P; R := R, p fi;
p := p+1 od:
R end:
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PROG
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(Sage)
P = {}
for p in (1..searchlimit):
q = sigma(p)//euler_phi(p)
if q not in P: P[q] = p
return sorted(P.values())
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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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