A097211 - OEIS

%I #13 Jul 27 2024 09:41:49

%S 1,2,4,10,8,44,16,184,218,32,400,752,3748,64,3392,3040,61064,128,

%T 27904,253808,12224,64594,57856,981520,256,226304,16450240,49024,

%U 16700300,954368,15722528,512,1822720,1055953664,196352,4278006328,15499264

%N a(n) = the number of sets of distinct positive integers with a least common multiple of A025487(n), i.e., A076078(A025487(n)).

%C The sequence A025487 contains the least number of each prime signature.

%C Sequence is a rearrangement of A097210 unless two or more members of A025487 are LCMs of an identical number of sets of distinct positive integers.

%H Amiram Eldar, <a href="/A097211/b097211.txt">Table of n, a(n) for n = 1..2534</a>

%t f[n_] := Block[{d = Divisors[n]}, Plus @@ (MoebiusMu[n/d](2^DivisorSigma[0, d] - 1))]; PrimeExponents[n_] := Flatten[ Table[ # [[2]], {1}] & /@ FactorInteger[n]]; lpe = {}; ln = {1}; Do[pe = Sort[PrimeExponents[n]]; If[ Position[lpe, pe] == {}, AppendTo[lpe, pe]; AppendTo[ln, f[n]]], {n, 1000}]; ln (* _Robert G. Wilson v_, Aug 14 2004 *)

%Y Cf. A025487, A076078, A097210.

%K nonn

%O 1,2

%A _Matthew Vandermast_, Aug 09 2004

%E Second comment edited by _Matthew Vandermast_, Oct 21 2008