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A376250
Numbers with a unique largest prime exponent (A356862) that are not prime powers (A246655).
2
12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 68, 72, 75, 76, 80, 84, 88, 90, 92, 96, 98, 99, 104, 108, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 144, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168, 171, 172, 175, 176, 184, 188, 189, 192, 198, 200
OFFSET
1,1
COMMENTS
First differs from A059404 at n = 55: A059404(55) = 180 = 2^2 * 3^2 * 5 is not a term of this sequence.
First differs from A360248 at n = 23: a(23) = 90 = 2 * 3^2 * 5 is not a term of A360248.
First differs from A332785 at n = 17: a(17) = 72 = 2^3 * 3^2 is not a term of A332785.
Numbers whose unordered prime signature (i.e., sorted, see A118914) ends with two different integers: {..., k, m} for some 1 <= k < m.
All the factorial numbers above 6 are terms.
The asymptotic density of this sequence is Sum_{k >= 1, p prime} (d(k+1, p) - d(k, p))/((p-1)*p^k) = 0.3660366524547281232052..., where d(k, p) = 0 for k = 1, and (1-1/p)/((1-1/p^k)*zeta(k)) for k > 1, is the density of terms that have in their prime factorization a prime p with the largest exponent that is > k.
LINKS
MATHEMATICA
Select[Range[2, 200], Length[e = FactorInteger[#][[;; , 2]]] > 1 && Count[e, Max[e]] == 1 &]
PROG
(PARI) is(k) = if (k == 1, 0, my(e = vecsort(factor(k)[, 2])); #e > 1 && e[#e] > e[#e-1]);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 17 2024
STATUS
approved