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%I #15 Oct 09 2017 11:12:29
%S 1,1,0,2,0,1,0,0,5,0,1,0,4,0,0,0,1,0,0,5,0,15,0,0,0,0,2,0,16,0,0,0,0,
%T 0,0,7,0,8,0,0,1,0,23,0,0,0,1,0,5,0,0,0,0,52,14,0,0,0,0,0,1,0,0,0,0,
%U 68,3,0,4,0,0,40,0,0,0,0,11,0,0,0,0,0,41
%N Number of factorizations into distinct squarefree factors indexed by prime signatures. A050326(A025487).
%C From _Michael De Vlieger_, Oct 06 2017: (Start)
%C Terms in A025487 that set records in this sequence: {1, 6, 30, 210, 420, 1260, 2310, 4620, 13860, 30030, 60060, 180180, 510510, 900900, 1021020, 3063060, 6126120, 9699690, ...}.
%C Conjecture: prime signatures corresponding to primorials A002110(i) with i > 1 set records in this sequence. (End)
%H Michael De Vlieger, <a href="/A050327/b050327.txt">Table of n, a(n) for n = 1..500</a>
%H Michael De Vlieger, <a href="/A050327/a050327.txt">Relations between A050327, A025487, and A002110.</a>
%F From _Michael De Vlieger_, Oct 06 2017: (Start)
%F a(n) = A050326(A025487(n)).
%F A050326(A002110(n)) = A000110(n).
%F (End)
%e From _Michael De Vlieger_, Oct 06 2017: (Start)
%e First 20 values, with numbers in column "r" records, and the last column the concatenation of exponents of standard form prime decomposition of A025487(n):
%e .
%e n a(n) r A025487(n) rev(A054841(A025487(n)))
%e --------------------------------------------
%e 1 1 1 1 0
%e 2 1 2 1
%e 3 0 4 2
%e 4 2 2 6 11
%e 5 0 8 3
%e 6 1 12 21
%e 7 0 16 4
%e 8 0 24 31
%e 9 5 3 30 111
%e 10 0 32 5
%e 11 1 36 22
%e 12 0 48 41
%e 13 4 60 211
%e 14 0 64 6
%e 15 0 72 32
%e 16 0 96 51
%e 17 1 120 311
%e 18 0 128 7
%e 19 0 144 42
%e 20 5 180 221
%e 21 0 192 61
%e 22 15 4 210 1111
%e (End)
%t f[n_] := If[n <= 1, {{}}, Join @@ Table[Map[Prepend[#, d] &, Select[f[n/d], Min @@ # > d &]], {d, Select[Rest@ Divisors@ n, SquareFreeQ]}]]; Length[f@ #] & /@ Prepend[#, 1] &@ Sort@ Map[Times @@ Flatten@ MapIndexed[ConstantArray[Prime@ First@ #2, #1] &, #] &, Union@ Table[Sort[FactorInteger[n][[All, -1]], Greater], {n, 2, Product[Prime@ i, {i, 7}]}]] (* _Michael De Vlieger_, Oct 06 2017, after _Gus Wiseman_ at A293243 *)
%Y Cf. A000110, A002110, A025487, A050326.
%K nonn
%O 1,4
%A _Christian G. Bower_, Oct 15 1999