A071389 Least number m such that cardinality of InvPhi(m) = prime(n).
1, 2, 8, 32, 48, 396, 72, 216, 1056, 1320, 240, 480, 15936, 3072, 7344, 2016, 3024, 9984, 22848, 3360, 13248, 9360, 4800, 9504, 9216, 23328, 7680, 53280, 12480, 29376, 91200, 159744, 22464, 228960, 29952, 179200, 47040, 68544, 15840, 20736, 61440
Offset: 1
Keywords
Examples
For n = 11: prime(11) = 31, Card(InvPhi(x)) = 31 for {240, 672, ...}; the smallest is 240 = a(11).
Links
- Amiram Eldar, Table of n, a(n) for n = 1..1000
- Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).
Programs
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PARI
lista(len) = {my(p = prime(len), v = vector(p, i, -!isprime(i)), c = 0, k = 1, i); while(c < len, i = invphiNum(k); if(i > 0 && i <= p && v[i] == 0, c++; v[i] = k); k++); select(x -> x > 0, v);} \\ Amiram Eldar, Nov 11 2024, using Max Alekseyev's invphi.gp
Formula
a(n) = Min{x; Card(InvPhi(x)) = prime(n), n-th prime}
Extensions
4 more terms from Emeric Deutsch, Jul 25 2005
More terms from Max Alekseyev, Apr 24 2010