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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). 8
1, 2, 6, 12, 30, 60, 210, 360, 420, 1260, 2310, 2520, 4620, 13860, 27720, 30030, 60060, 75600, 138600, 180180, 360360, 510510, 831600, 900900, 1021020, 1801800, 3063060, 6126120, 9699690, 10810800, 15315300, 19399380, 30630600, 37837800 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Members m of A025487 such that A181819(m) is also a member of A025487.
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 *)
CROSSREFS
Intersection of A025487 and A179983.
Subsequence of A129912 and A181826.
Includes all members of A182862.
Positions of first appearances in A353742, unordered version A238747.
A001222 counts prime factors with multiplicity, distinct A001221.
A003963 gives product of prime indices.
A005361 gives product of prime signature, firsts A353500 (sorted A085629).
A056239 adds up prime indices, row sums of A112798 and A296150.
A124010 gives prime signature, sorted A118914.
A130091 lists numbers with distinct prime exponents, counted by A098859.
A181819 gives prime shadow, with an inverse A181821.
A182850 gives frequency depth of prime indices, counted by A225485.
A323014 gives adjusted frequency depth of prime indices, counted by A325280.
Sequence in context: A331552 A129912 A283477 * A161507 A335711 A032177
KEYWORD
nonn
AUTHOR
Matthew Vandermast, Jan 14 2011
STATUS
approved

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Last modified July 12 23:13 EDT 2024. Contains 374257 sequences. (Running on oeis4.)