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A355667
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Least number phi(k) such that n * phi(k) < k, where phi is Euler's totient function.
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0
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OFFSET
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1,2
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COMMENTS
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a(n) is the Euler totient of A091456(n). Useful for calculating a simple upper bound of the inverse phi function.
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LINKS
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Table of n, a(n) for n=1..9.
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FORMULA
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a(n) = A000010(A091456(n)).
a(n) = A000010(A091439(n+1)).
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EXAMPLE
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If we know n=276, then all numbers k with phi(k)=n will satisfy k < 5*n since m=a(5) is the first number in the sequence with n < m.
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MATHEMATICA
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a[n_] := Module[{k = 1, p = 1, e}, While[k <= n*(e = EulerPhi[k]), p = NextPrime[p]; k *= p]; e]; Array[a, 9] (* Amiram Eldar, Jul 13 2022 *)
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PROG
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(PARI) a(n)=my(k=1); forprime(p=2, , if(n*eulerphi(k)<k, return(eulerphi(k)), k*=p)
(CoCoA 5) define a(n) k := 1; p := 1; while k <= n*EulerTotient(k) do p := NextPrime(p); k := k*p; endwhile; return EulerTotient(k); enddefine;
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CROSSREFS
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Totients of A091456 or A091439.
Sequence in context: A356658 A279239 A279109 * A183070 A032116 A088181
Adjacent sequences: A355664 A355665 A355666 * A355668 A355669 A355670
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KEYWORD
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nonn
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AUTHOR
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Nico Mexis, Jul 13 2022
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STATUS
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approved
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