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 A350140 #10 Jan 07 2022 15:55:13
%S A350140 60,84,120,132,140,150,156,168,204,220,228,240,260,264,270,276,280,
%T A350140 294,300,308,312,315,336,340,348,364,372,378,380,408,420,440,444,456,
%U A350140 460,476,480,490,492,495,516,520,528,532,540,552,560,564,572,580,585,588
%N A350140 Nonsquarefree numbers whose prime signature has at least one odd part other the first or last.
%C A350140 A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization.
%C A350140 Also Heinz numbers of non-weakly alternating non-strict integer partitions, where we define a sequence to be weakly alternating if it is alternately weakly increasing and weakly decreasing, starting with either. These partitions are counted by A349796. This sequence involves the somewhat degenerate case where no strict increases are allowed.
%F A350140 Complement of A005117 in A349794.
%e A350140 The terms together with their Heinz partitions begin (A-E = 10-14):
%e A350140 60: (3211) 276: (9211) 420: (43211)
%e A350140 84: (4211) 280: (43111) 440: (53111)
%e A350140 120: (32111) 294: (4421) 444: (C211)
%e A350140 132: (5211) 300: (33211) 456: (82111)
%e A350140 140: (4311) 308: (5411) 460: (9311)
%e A350140 150: (3321) 312: (62111) 476: (7411)
%e A350140 156: (6211) 315: (4322) 480: (3211111)
%e A350140 168: (42111) 336: (421111) 490: (4431)
%e A350140 204: (7211) 340: (7311) 492: (D211)
%e A350140 220: (5311) 348: (A211) 495: (5322)
%e A350140 228: (8211) 364: (6411) 516: (E211)
%e A350140 240: (321111) 372: (B211) 520: (63111)
%e A350140 260: (6311) 378: (42221) 528: (521111)
%e A350140 264: (52111) 380: (8311) 532: (8411)
%e A350140 270: (32221) 408: (72111) 540: (322211)
%t A350140 Select[Range[300],!SquareFreeQ[#]&&PrimeNu[#]>1&& !And@@EvenQ/@Take[Last/@FactorInteger[#],{2,-2}]&]
%Y A350140 Including all nonsquarefree numbers gives A013929, complement A005117.
%Y A350140 Subsets include A088860 and A110286.
%Y A350140 Signatures of this type are counted by A274230, complement A027383.
%Y A350140 The strict instead of non-strict version is A336568, counted by A347548.
%Y A350140 A version for compositions allowing strict is A349057, counted by A349053.
%Y A350140 Allowing strict partitions gives A349794, counted by A349061.
%Y A350140 These partitions are counted by A349796.
%Y A350140 The complement in nonsquarefree partitions is A350137, counted by A349795.
%Y A350140 A000041 = integer partitions, strict A000009.
%Y A350140 A001250 = alternating permutations, ranked by A349051, complement A348615.
%Y A350140 A003242 = Carlitz (anti-run) compositions.
%Y A350140 A025047/A025048/A025049 = alternating compositions, ranked by A345167.
%Y A350140 A056239 adds up prime indices, row sums of A112798, row lengths A001222.
%Y A350140 A096441 = weakly alternating 0-appended partitions.
%Y A350140 A124010 = prime signature, sorted A118914.
%Y A350140 A345164 = alternating permutations of prime indices, complement A350251.
%Y A350140 A345170 = partitions w/ an alternating permutation, ranked by A345172.
%Y A350140 A349052/A129852/A129853 = weakly alternating compositions.
%Y A350140 A349056 = weakly alternating permutations of prime indices.
%Y A350140 A349058 = weakly alternating patterns, complement A350138.
%Y A350140 A349060 = weakly alternating partitions, strong A349801.
%Y A350140 A349798 = weakly but not strongly alternating perms of prime indices.
%Y A350140 Cf. A000111, A047967, A333213, A335448, A344615, A344653, A345173, A349054, A349059, A349797, A349799.
%K A350140 nonn
%O A350140 1,1
%A A350140 _Gus Wiseman_, Dec 25 2021