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A355667 Least number phi(k) such that n * phi(k) < k, where phi is Euler's totient function. 1
1, 2, 8, 48, 5760, 36495360, 1854081073152000, 400440702414394285778534400000, 165062110921422523175104166476600499887194872217600000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) is the Euler totient of A091456(n). Useful for calculating a simple upper bound of the inverse phi function.
LINKS
John Abbott and Nico Mexis, Cyclotomic Factors and LRS-Degeneracy, arXiv:2403.08751 [math.AC], 2024. See pp. 9, 24.
FORMULA
a(n) = A000010(A091456(n)).
a(n) = A000010(A091439(n+1)).
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(PARI) a(n)=my(k=1); forprime(p=2, , if(n*eulerphi(k)<k, return(eulerphi(k)), k*=p)
(CoCoA) // 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;
CROSSREFS
Totients of A091456 or A091439.
Sequence in context: A356658 A279239 A279109 * A366239 A364592 A183070
KEYWORD
nonn
AUTHOR
Nico Mexis, Jul 13 2022
STATUS
approved

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Last modified June 19 05:57 EDT 2024. Contains 373492 sequences. (Running on oeis4.)