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 A181822 a(n) = member of A025487 whose prime signature is conjugate to the prime signature of A025487(n). 16
 1, 2, 6, 4, 30, 12, 210, 60, 8, 2310, 36, 420, 24, 30030, 180, 4620, 120, 510510, 1260, 72, 60060, 16, 900, 840, 9699690, 13860, 360, 1021020, 48, 6300, 9240, 223092870, 180180, 2520, 19399380, 240, 69300, 216, 120120, 6469693230, 1800, 3063060, 144, 44100, 27720, 446185740, 1680, 900900, 1080, 2042040, 200560490130, 12600, 58198140, 32, 720 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A permutation of the members of A025487. If integers m and n have conjugate prime signatures, then A001222(m) = A001222(n), A071625(m) = A071625(n), A085082(m) = A085082(n), and A181796(m) = A181796(n). LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Conjugate Partition FORMULA If A025487(n) = Product p(i)^e(i), then a(n) = Product A002110(e(i)). I.e., a(n) = A108951(A181819(A025487(n))). a(n) also equals A108951(A181820(n)). EXAMPLE A025487(5) = 8 = 2^3 has a prime signature of (3). The partition that is conjugate to (3) is (1,1,1), and the member of A025487 with that prime signature is 30 = 2*3*5 (or 2^1*3^1*5^1).  Therefore, a(5) = 30. MATHEMATICA f[n_] := Block[{ww, dec}, dec[x_] := Apply[Times, MapIndexed[Prime[First@ #2]^#1 &, x]]; ww = NestList[Append[#, 1] &, {1}, # - 1] &[-2 + Length@ NestWhileList[NextPrime@ # &, 1, Times @@ {##} <= n &, All] ]; {{{0}}}~Join~Map[Block[{w = #, k = 1}, Sort@ Apply[Join, {{ConstantArray[1, Length@ w]}, If[Length@ # == 0, #, #[[1]]] }] &@ Reap[Do[If[# <= n, Sow[w]; k = 1, If[k >= Length@ w, Break[], k++]] &@ dec@ Set[w, If[k == 1, MapAt[# + 1 &, w, k], PadLeft[#, Length@ w, First@ #] &@ Drop[MapAt[# + Boole[i > 1] &, w, k], k - 1] ]], {i, Infinity}] ][[-1]] ] &, ww]]; Sort[Map[{Times @@ MapIndexed[Prime[First@ #2]^#1 &, #], Times @@ MapIndexed[Prime[First@ #2]^#1 &, Table[LengthWhile[#1, # >= j &], {j, #2}]] & @@ {#, Max[#]}} &, Join @@ f[2310]]][[All, -1]] (* Michael De Vlieger, Oct 16 2018 *) PROG (PARI) partitionConj(v)=vector(v[1], i, sum(j=1, #v, v[j]>=i)) primeSignature(n)=vecsort(factor(n)[, 2]~, , 4) f(n)=if(n==1, return(1)); my(e=partitionConj(primeSignature(n))~); factorback(concat(Mat(primes(#e)~), e)) A025487=[2, 4, 6, 8, 12, 16, 24, 30, 32, 36, 48, 60, 64, 72, 96, 120, 128, 144, 180, 192, 210, 216, 240, 256, 288, 360, 384, 420, 432, 480, 512, 576, 720, 768]; concat(1, apply(f, A025487)) \\ Charles R Greathouse IV, Jun 02 2016 CROSSREFS Other rearrangements of A025487 include A036035, A059901, A063008, A077569, A085988, A086141, A087443, A108951, A181821. A181825 lists members of A025487 with self-conjugate prime signatures.  See also A181823-A181824, A181826-A181827. Sequence in context: A064538 A002790 A108951 * A174940 A293011 A108435 Adjacent sequences:  A181819 A181820 A181821 * A181823 A181824 A181825 KEYWORD nonn,look AUTHOR Matthew Vandermast, Dec 07 2010 STATUS approved

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Last modified June 1 00:27 EDT 2020. Contains 334756 sequences. (Running on oeis4.)