cp's OEIS Frontend

A369150 Numbers k neither squarefree nor prime powers such that A053669(k) < k/rad(k) < A119288(k) that are not odd numbers of the form lpf(k)*rad(k), where lpf(k) = A020639(k) and rad(k) = A007947(k).

%I A369150 #25 Jan 23 2024 19:12:12
%S A369150 40,56,88,104,136,152,176,184,208,232,248,272,280,296,297,304,328,344,
%T A369150 351,368,376,424,440,459,464,472,488,496,513,520,536,544,568,584,592,
%U A369150 608,616,621,632,656,664,680,688,712,728,736,752,760,776,783,808,824,837
%N A369150 Numbers k neither squarefree nor prime powers such that A053669(k) < k/rad(k) < A119288(k) that are not odd numbers of the form lpf(k)*rad(k), where lpf(k) = A020639(k) and rad(k) = A007947(k).
%C A369150 Numbers k neither squarefree nor prime powers such that the smallest nondivisor prime q < k/rad(k) < p, the second smallest prime factor of k where k/rad(k) != lpf(k).
%C A369150 Even k implies A053669(k) = 3, odd k implies A053669(k) = 2.
%C A369150 Sequence does not contain k divisible by 6; sequence does not meet A055932.
%C A369150 Proper subset of A367455.
%H A369150 Michael De Vlieger, <a href="/A369150/b369150.txt">Table of n, a(n) for n = 1..10000</a>
%F A369150 This sequence is { A364997 \ A366460 } = { A364997 \ A366825 }.
%e A369150 a(1) = 40 = 2^3 * 5, since 3 < 4 < 5 and 4 != 2.
%e A369150 a(2) = 56 = 2^3 * 7, since 3 < 4 < 7 and 4 != 2.
%e A369150 a(7) = 176 = 2^4 * 11, since 3 < 8 < 11 and 8 != 2.
%e A369150 a(15) = 297 = 3^3 * 11, since 2 < 9 < 11 and 9 != 3.
%e A369150 a(248) = 3625 = 5^3 * 29, since 2 < 25 < 29 and 25 != 5, etc.
%t A369150 s = Select[Range[1000], Nor[PrimePowerQ[#], SquareFreeQ[#]] &];
%t A369150 Select[s,
%t A369150   And[#3 < #1 < #2, #1 != #4] & @@
%t A369150   {#1/(Times @@ #2), #2[[2]], #3, First[#2]} & @@
%t A369150   {#, FactorInteger[#][[All, 1]],
%t A369150     If[OddQ[#], 2, q = 3; While[Divisible[#, q], q = NextPrime[q]]; q]} &]
%Y A369150 Cf. A007947, A020639, A053669, A119288, A126706, A364997, A366460, A366825, A367455.
%K A369150 nonn
%O A369150 1,1
%A A369150 _Michael De Vlieger_, Jan 20 2024