cp's OEIS Frontend

A386808 Numbers that have exactly one exponent in their prime factorization that is equal to 5.

%I A386808 #7 Aug 03 2025 16:05:29
%S A386808 32,96,160,224,243,288,352,416,480,486,544,608,672,736,800,864,928,
%T A386808 972,992,1056,1120,1184,1215,1248,1312,1376,1440,1504,1568,1632,1696,
%U A386808 1701,1760,1824,1888,1944,1952,2016,2080,2144,2208,2272,2336,2400,2430,2464,2528
%N A386808 Numbers that have exactly one exponent in their prime factorization that is equal to 5.
%C A386808 Subsequence of A362841 and first differs from it at n = 145: A362841(145) = 7776 = 2^5 * 3 ^ 5 is not a term of this sequence.
%C A386808 The asymptotic density of this sequence is Product_{p prime} (1 - 1/p^5 + 1/p^6) * Sum_{p prime} (p-1)/(p^6 - p + 1) = 0.0185875810803524107305... (Elma and Martin, 2024).
%H A386808 Amiram Eldar, <a href="/A386808/b386808.txt">Table of n, a(n) for n = 1..10000</a>
%H A386808 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 A386808 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%t A386808 f[p_, e_] := If[e == 5, 1, 0]; s[1] = 0; s[n_] := Plus @@ f @@@ FactorInteger[n]; Select[Range[3000], s[#] == 1 &]
%o A386808 (PARI) isok(k) = vecsum(apply(x -> if(x == 5, 1, 0), factor(k)[, 2])) == 1;
%Y A386808 Cf. A362841.
%Y A386808 Numbers that have exactly one exponent in their prime factorization that is equal to k: A119251 (k=1), A386796 (k=2), A386800 (k=3), A386804 (k=4), this sequence (k=5).
%Y A386808 Numbers that have exactly m exponents in their prime factorization that are equal to 5: A386807 (m=0), this sequence (m=1), A386809 (m=2), A386810 (m=3).
%K A386808 nonn,easy
%O A386808 1,1
%A A386808 _Amiram Eldar_, Aug 03 2025