A355667 Least number phi(k) such that n * phi(k) < k, where phi is Euler's totient function.
1, 2, 8, 48, 5760, 36495360, 1854081073152000, 400440702414394285778534400000, 165062110921422523175104166476600499887194872217600000000
Offset: 1
Keywords
Examples
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.
Links
- Nico Mexis, Table of n, a(n) for n = 1..13
- John Abbott and Nico Mexis, Cyclotomic Factors and LRS-Degeneracy, arXiv:2403.08751 [math.AC], 2024. See pp. 9, 24.
Programs
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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;
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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 *) -
PARI
a(n)=my(k=1); forprime(p=2, , if(n*eulerphi(k)
Comments