This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A374277 #28 Jul 26 2024 15:17:25
%S A374277 2,3,4,5,8,9,14,16,21,22,25,26,27,28,32,33,34,35,38,39,44,46,51,52,55,
%T A374277 56,57,58,62,63,64,65,68,69,74,76,81,82,85,86,87,88,92,93,94,95,98,99,
%U A374277 104,106,111,112,115,116,117,118,122,123,124,125,128,129,134
%N A374277 Numbers k divisible by exactly one of the prime factors of 30.
%C A374277 Numbers k congruent to r (mod 30), where r is in {2, 3, 4, 5, 8, 9, 14, 16, 21, 22, 25, 26, 27, 28}, residues r = p^m mod 30 and r = (30 - p^m) mod 30.
%C A374277 The asymptotic density of this sequence is 7/15. - _Amiram Eldar_, Jul 26 2024
%H A374277 Michael De Vlieger, <a href="/A374277/b374277.txt">Table of n, a(n) for n = 1..10000</a>
%H A374277 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
%F A374277 Intersection of this sequence and 5-smooth numbers (A051037) is A306044 \ {1}.
%e A374277 8 is in this sequence since it is even and a multiple of neither 3 nor 5.
%e A374277 10 is not in this sequence since 10 = 2*5; both 2 and 5 divide 30.
%e A374277 14 is in this sequence since it is even and a multiple of neither 3 nor 5, etc.
%t A374277 s = Prime@ Range[3]; k = Times @@ s; r = Union[#, k - #] &@ Flatten@ Map[PowerRange[#, k, #] &, s]; m = Length[r]; Array[k*#1 + r[[1 + #2]] & @@ QuotientRemainder[# - 1, m] &, 60]
%o A374277 (PARI) is(k) = isprime(gcd(k, 30)); \\ _Amiram Eldar_, Jul 26 2024
%Y A374277 Cf. A047228, A051037, A306044.
%K A374277 nonn,easy
%O A374277 1,1
%A A374277 _Michael De Vlieger_, Jul 26 2024