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 A182863 #31 Feb 16 2025 08:33:13
%S A182863 1,2,6,12,30,60,210,360,420,1260,2310,2520,4620,13860,27720,30030,
%T A182863 60060,75600,138600,180180,360360,510510,831600,900900,1021020,
%U A182863 1801800,3063060,6126120,9699690,10810800,15315300,19399380,30630600,37837800
%N A182863 Members m of A025487 such that, if k appears in m's prime signature, k-1 appears at least as often as k (for any integer k > 1).
%C A182863 Members m of A025487 such that A181819(m) is also a member of A025487.
%C A182863 If prime signatures are considered as partitions, these are the members of A025487 whose prime signature is conjugate to the prime signature of a member of A181818.
%C A182863 Also the least number with each sorted prime metasignature, where a number's metasignature is the sequence of multiplicities of exponents in its prime factorization. For example, 2520 has prime indices {1,1,1,2,2,3,4}, sorted prime signature {1,1,2,3}, and sorted prime metasignature {1,1,2}. - _Gus Wiseman_, May 21 2022
%H A182863 David A. Corneth, <a href="/A182863/b182863.txt">Table of n, a(n) for n = 1..10000</a> (first 1444 terms from Amiram Eldar)
%H A182863 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConjugatePartition.html">Conjugate Partition</a>.
%e A182863 The prime signature of 360360 = 2^3*3^2*5*7*11*13 is (3,2,1,1,1,1). 2 appears as many times as 3 in 360360's prime signature, and 1 appears more times than 2. Since 360360 is also a member of A025487, it is a member of this sequence.
%e A182863 From _Gus Wiseman_, May 21 2022: (Start)
%e A182863 The terms together with their sorted prime signatures and sorted prime metasignatures begin:
%e A182863 1: {} -> {} -> {}
%e A182863 2: {1} -> {1} -> {1}
%e A182863 6: {1,2} -> {1,1} -> {2}
%e A182863 12: {1,1,2} -> {1,2} -> {1,1}
%e A182863 30: {1,2,3} -> {1,1,1} -> {3}
%e A182863 60: {1,1,2,3} -> {1,1,2} -> {1,2}
%e A182863 210: {1,2,3,4} -> {1,1,1,1} -> {4}
%e A182863 360: {1,1,1,2,2,3} -> {1,2,3} -> {1,1,1}
%e A182863 420: {1,1,2,3,4} -> {1,1,1,2} -> {1,3}
%e A182863 1260: {1,1,2,2,3,4} -> {1,1,2,2} -> {2,2}
%e A182863 2310: {1,2,3,4,5} -> {1,1,1,1,1} -> {5}
%e A182863 2520: {1,1,1,2,2,3,4} -> {1,1,2,3} -> {1,1,2}
%e A182863 4620: {1,1,2,3,4,5} -> {1,1,1,1,2} -> {1,4}
%e A182863 13860: {1,1,2,2,3,4,5} -> {1,1,1,2,2} -> {2,3}
%e A182863 27720: {1,1,1,2,2,3,4,5} -> {1,1,1,2,3} -> {1,1,3}
%e A182863 30030: {1,2,3,4,5,6} -> {1,1,1,1,1,1} -> {6}
%e A182863 60060: {1,1,2,3,4,5,6} -> {1,1,1,1,1,2} -> {1,5}
%e A182863 (End)
%t A182863 nn=1000;
%t A182863 r=Table[Sort[Length/@Split[Sort[Last/@If[n==1,{},FactorInteger[n]]]]],{n,nn}];
%t A182863 Select[Range[nn],!MemberQ[Take[r,#-1],r[[#]]]&] (* _Gus Wiseman_, May 21 2022 *)
%Y A182863 Intersection of A025487 and A179983.
%Y A182863 Subsequence of A129912 and A181826.
%Y A182863 Includes all members of A182862.
%Y A182863 Positions of first appearances in A353742, unordered version A238747.
%Y A182863 A001222 counts prime factors with multiplicity, distinct A001221.
%Y A182863 A003963 gives product of prime indices.
%Y A182863 A005361 gives product of prime signature, firsts A353500 (sorted A085629).
%Y A182863 A056239 adds up prime indices, row sums of A112798 and A296150.
%Y A182863 A124010 gives prime signature, sorted A118914.
%Y A182863 A130091 lists numbers with distinct prime exponents, counted by A098859.
%Y A182863 A181819 gives prime shadow, with an inverse A181821.
%Y A182863 A182850 gives frequency depth of prime indices, counted by A225485.
%Y A182863 A323014 gives adjusted frequency depth of prime indices, counted by A325280.
%Y A182863 Cf. A000040, A055932, A070175, A097318, A304678, A325238, A353507, A353745.
%K A182863 nonn
%O A182863 1,2
%A A182863 _Matthew Vandermast_, Jan 14 2011