cp's OEIS Frontend

A381316 Numbers whose powerful part (A057521) is a power of a prime with an exponent >= 3 (A246549).

%I A381316 #10 Feb 21 2025 08:24:05
%S A381316 8,16,24,27,32,40,48,54,56,64,80,81,88,96,104,112,120,125,128,135,136,
%T A381316 152,160,162,168,176,184,189,192,208,224,232,240,243,248,250,256,264,
%U A381316 270,272,280,296,297,304,312,320,328,336,343,344,351,352,368,375,376,378
%N A381316 Numbers whose powerful part (A057521) is a power of a prime with an exponent >= 3 (A246549).
%C A381316 First differs from A344653 and A345193 at n = 17: a(17) = 120 is not a term of these sequences.
%C A381316 Numbers whose prime signature (A118914) is of the form {1, 1, ..., m} with m >= 3, i.e., any number (including zero) of 1's and then a single number >= 3.
%C A381316 The asymptotic density of this sequence is (1/zeta(2)) * Sum_{p prime} 1/(p*(p^2-1)) = A369632 / A013661 = 0.13463358553764438661... .
%H A381316 Amiram Eldar, <a href="/A381316/b381316.txt">Table of n, a(n) for n = 1..10000</a>
%t A381316 q[n_] := Module[{e = ReverseSort[FactorInteger[n][[;; , 2]]]}, e[[1]] > 2 && (Length[e] == 1 || e[[2]] == 1)]; Select[Range[1000], q]
%o A381316 (PARI) isok(k) = if(k == 1, 0, my(e = vecsort(factor(k)[, 2], , 4)); e[1] > 2 && (#e == 1 || e[2] == 1));
%Y A381316 Complement of A060687 within A190641.
%Y A381316 Cf. A013661, A057521, A246549, A369632.
%Y A381316 Cf. A344653, A345193.
%Y A381316 Subsequences: A030078, A030514, A030516, A030629, A030631, A050997, A056824, A065036, A079395, A092759, A138031, A178739, A178740, A179644, A179645, A179664, A179665, A179667, A179668, A179670, A179672, A179692, A179693, A179696, A179704, A179747, A189975, A189984, A189987, A190110, A190292, A190378, A190383, A190388, A190473, A381312.
%K A381316 nonn,easy
%O A381316 1,1
%A A381316 _Amiram Eldar_, Feb 19 2025