A097211 a(n) = the number of sets of distinct positive integers with a least common multiple of A025487(n), i.e., A076078(A025487(n)).

1, 2, 4, 10, 8, 44, 16, 184, 218, 32, 400, 752, 3748, 64, 3392, 3040, 61064, 128, 27904, 253808, 12224, 64594, 57856, 981520, 256, 226304, 16450240, 49024, 16700300, 954368, 15722528, 512, 1822720, 1055953664, 196352, 4278006328, 15499264

Offset: 1

Author

Matthew Vandermast, Aug 09 2004

Keywords

• nonn

Comments

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

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.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2534

Crossrefs

Cf. A025487, A076078, A097210.

Programs

Mathematica

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 *)

Extensions

Second comment edited by Matthew Vandermast, Oct 21 2008