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 A050322 Number of factorizations indexed by prime signatures: A001055(A025487). 7

%I

%S 1,1,2,2,3,4,5,7,5,7,9,12,11,11,16,19,21,15,29,26,30,15,31,38,22,47,

%T 52,45,36,57,64,30,77,98,67,74,97,66,105,42,109,118,92,109,171,97,141,

%U 162,137,165,56,212,181,52,198,189,289,139,250,257,269,254,77,382,267

%N Number of factorizations indexed by prime signatures: A001055(A025487).

%C For A025487(m) = 2^k = A000079(k), we have a(m) = A000041(k).

%C Is a(k) = A000110(k) for A025487(m) = A002110(k)?

%H R. J. Mathar and Michael De Vlieger, <a href="/A050322/b050322.txt">Table of n, a(n) for n = 1..5000</a> (First 300 terms from _R. J. Mathar_)

%p A050322 := proc(n)

%p A001055(A025487(n)) ;

%p end proc: # _R. J. Mathar_, May 25 2017

%t c[1, r_] := c[1, r] = 1; c[n_, r_] := c[n, r] = Module[{d, i}, d = Select[Divisors[n], 1 < # <= r &]; Sum[c[n/d[[i]], d[[i]]], {i, 1, Length[d]}]]; Map[c[#, #] &, Union@ Table[Times @@ MapIndexed[If[n == 1, 1, Prime[First@ #2]]^#1 &, Sort[FactorInteger[n][[All, -1]], Greater]], {n, Product[Prime@ i, {i, 6}]}]] (* _Michael De Vlieger_, Jul 10 2017, after _Dean Hickerson_ at A001055 *)

%Y Cf. A000041, A000079, A000110, A001055, A002110, A025487.

%K nonn

%O 1,3

%A _Christian G. Bower_, Oct 15 1999

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Last modified June 18 18:52 EDT 2019. Contains 324215 sequences. (Running on oeis4.)