cp's OEIS Frontend

A386797 Numbers that have exactly two exponents in their prime factorization that are equal to 2.

%I A386797 #7 Aug 03 2025 10:20:50
%S A386797 36,100,180,196,225,252,300,396,441,450,468,484,588,612,676,684,700,
%T A386797 828,882,980,1044,1089,1100,1116,1156,1225,1260,1300,1332,1444,1452,
%U A386797 1476,1521,1548,1575,1692,1700,1800,1900,1908,1980,2028,2100,2116,2124,2156,2178,2196
%N A386797 Numbers that have exactly two exponents in their prime factorization that are equal to 2.
%C A386797 First differs from its subsequence A375144 at n = 38: a(38) = 1800 = 2^3 * 3^2 * 5^2 is not a term of A375144.
%C A386797 Numbers k such that A369427(k) = 2.
%C A386797 The asymptotic density of this sequence is Product_{p primes} (1 - 1/p^2 + 1/p^3) * ((Sum_{p prime} (p-1)/(p^3 - p + 1))^2 - Sum_{p prime} ((p-1)^2/(p^3 - p + 1)^2)) / 2 = 0.023701044250873975412... (the product is A330596) (Elma and Martin, 2024).
%H A386797 Amiram Eldar, <a href="/A386797/b386797.txt">Table of n, a(n) for n = 1..10000</a>
%H A386797 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 A386797 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%t A386797 f[p_, e_] := If[e == 2, 1, 0]; s[1] = 0; s[n_] := Plus @@ f @@@ FactorInteger[n]; Select[Range[2200], s[#] == 2 &]
%o A386797 (PARI) isok(k) = vecsum(apply(x -> if(x == 2, 1, 0), factor(k)[, 2])) == 2;
%Y A386797 A375144 is a subsequence.	
%Y A386797 Cf. A330596, A369427.
%Y A386797 Numbers that have exactly two exponents in their prime factorization that are equal to k: this sequence (k=2), A386801 (k=3), A386805 (k=4), A386809 (k=5).
%Y A386797 Numbers that have exactly m exponents in their prime factorization that are equal to 2: A337050 (m=0), A386796 (m=1), this sequence (m=2), A386798 (m=3).
%K A386797 nonn,easy
%O A386797 1,1
%A A386797 _Amiram Eldar_, Aug 02 2025