cp's OEIS Frontend

A386804 Numbers that have exactly one exponent in their prime factorization that is equal to 4.

%I A386804 #6 Aug 03 2025 16:09:48
%S A386804 16,48,80,81,112,144,162,176,208,240,272,304,324,336,368,400,405,432,
%T A386804 464,496,528,560,567,592,624,625,648,656,688,720,752,784,810,816,848,
%U A386804 880,891,912,944,976,1008,1040,1053,1072,1104,1134,1136,1168,1200,1232,1250
%N A386804 Numbers that have exactly one exponent in their prime factorization that is equal to 4.
%C A386804 Subsequence of A336595 and first differs from it at n = 21: A336595(21) = 512 = 2^9 is not a term of this sequence.
%C A386804 The asymptotic density of this sequence is Product_{p prime} (1 - 1/p^4 + 1/p^5) * Sum_{p prime} (p-1)/(p^5 - p + 1) = 0.04058504714976055893... (Elma and Martin, 2024).
%H A386804 Amiram Eldar, <a href="/A386804/b386804.txt">Table of n, a(n) for n = 1..10000</a>
%H A386804 Ertan Elma and Greg Martin, <a href="https://doi.org/10.4153/S0008439524000584">Distribution of the number of prime factors with a given multiplicity</a>, Canadian Mathematical Bulletin, Vol. 67, No. 4 (2024), pp. 1107-1122; <a href="https://arxiv.org/abs/2406.04574">arXiv preprint</a>, arXiv:2406.04574 [math.NT], 2024.
%H A386804 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%t A386804 f[p_, e_] := If[e == 4, 1, 0]; s[1] = 0; s[n_] := Plus @@ f @@@ FactorInteger[n]; Select[Range[1300], s[#] == 1 &]
%o A386804 (PARI) isok(k) = vecsum(apply(x -> if(x == 4, 1, 0), factor(k)[, 2])) == 1;
%Y A386804 Subsequence of A336595.
%Y A386804 Numbers that have exactly one exponent in their prime factorization that is equal to k: A119251 (k=1), A386796 (k=2), A386800 (k=3), this sequence (k=4), A386808 (k=5).
%Y A386804 Numbers that have exactly m exponents in their prime factorization that are equal to 4: A386803 (m=0), this sequence (m=1), A386805 (m=2), A386806 (m=3).
%K A386804 nonn,easy
%O A386804 1,1
%A A386804 _Amiram Eldar_, Aug 03 2025