OFFSET
1,2
COMMENTS
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.
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
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1444 terms from Amiram Eldar)
Eric Weisstein's World of Mathematics, Conjugate Partition.
EXAMPLE
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.
From Gus Wiseman, May 21 2022: (Start)
The terms together with their sorted prime signatures and sorted prime metasignatures begin:
1: {} -> {} -> {}
2: {1} -> {1} -> {1}
6: {1,2} -> {1,1} -> {2}
12: {1,1,2} -> {1,2} -> {1,1}
30: {1,2,3} -> {1,1,1} -> {3}
60: {1,1,2,3} -> {1,1,2} -> {1,2}
210: {1,2,3,4} -> {1,1,1,1} -> {4}
360: {1,1,1,2,2,3} -> {1,2,3} -> {1,1,1}
420: {1,1,2,3,4} -> {1,1,1,2} -> {1,3}
1260: {1,1,2,2,3,4} -> {1,1,2,2} -> {2,2}
2310: {1,2,3,4,5} -> {1,1,1,1,1} -> {5}
2520: {1,1,1,2,2,3,4} -> {1,1,2,3} -> {1,1,2}
4620: {1,1,2,3,4,5} -> {1,1,1,1,2} -> {1,4}
13860: {1,1,2,2,3,4,5} -> {1,1,1,2,2} -> {2,3}
27720: {1,1,1,2,2,3,4,5} -> {1,1,1,2,3} -> {1,1,3}
30030: {1,2,3,4,5,6} -> {1,1,1,1,1,1} -> {6}
60060: {1,1,2,3,4,5,6} -> {1,1,1,1,1,2} -> {1,5}
(End)
MATHEMATICA
nn=1000;
r=Table[Sort[Length/@Split[Sort[Last/@If[n==1, {}, FactorInteger[n]]]]], {n, nn}];
Select[Range[nn], !MemberQ[Take[r, #-1], r[[#]]]&] (* Gus Wiseman, May 21 2022 *)
KEYWORD
nonn
AUTHOR
Matthew Vandermast, Jan 14 2011
STATUS
approved