cp's OEIS Frontend

A157928 a(n) = 0 if n < 2, = 1 otherwise.

%I A157928 #40 Jul 03 2025 14:09:24
%S A157928 0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A157928 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A157928 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A157928 a(n) = 0 if n < 2, = 1 otherwise.
%C A157928 A characteristic function which indicates whether n has a prime factorization n = product p_i^e_i where p_i are primes (A000040) and e_i nonnegative exponents, at least one e_i nonzero.
%C A157928 a(n), n>=1, is also generated by the following Dirichlet convolutions:
%C A157928   a(n) = A157658(n) * A000012(n),
%C A157928   a(n) = A008683(n) * A032741(n).
%C A157928 a(n) appears as a factor in the following Dirichlet convolutions:
%C A157928   a(n) * A000010(n) = A051953(n),
%C A157928   a(n) * A000027(n) = A001065(n),
%C A157928   a(n) * A000012(n) = A032741(n).
%C A157928 a(n) is also both the number of disconnected 0-regular graphs on n vertices and the number of disconnected 1-regular graphs on 2n vertices. - _Jason Kimberley_, Sep 27 2011
%C A157928 Partial sums of A185012. - _Jason Kimberley_, Oct 15 2011
%C A157928 Decimal expansion of 1/900. - _Elmo R. Oliveira_, May 05 2024
%H A157928 J. S. Kimberley, <a href="/wiki/User:Jason_Kimberley/D_k-reg_girth_ge_g_index">Index of sequences counting disconnected k-regular simple graphs with girth at least g</a>.
%H A157928 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A157928 a(n) = A057427(n-1) for n >= 2.
%F A157928 From _Elmo R. Oliveira_, Jul 20 2024: (Start)
%F A157928 G.f.: x^2/(1-x).
%F A157928 E.g.f.: exp(x) - x - 1. (End)
%t A157928 PadRight[{0,0},120,{1}] (* _Harvey P. Dale_, Jun 03 2019 *)
%Y A157928 Cf. A000010, A000012, A000027, A000040, A001065, A008683, A032741, A051953, A057427, A157658, A185012.
%K A157928 nonn,easy
%O A157928 0,1
%A A157928 _Jaroslav Krizek_, Mar 09 2009
%E A157928 Definition simplified by _R. J. Mathar_, May 17 2010