A157928 - OEIS

A157928

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

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, 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, 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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

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.

a(n), n>=1, is also generated by the following Dirichlet convolutions:

a(n) = A157658(n) * A000012(n),

a(n) = A008683(n) * A032741(n).

a(n) appears as a factor in the following Dirichlet convolutions:

a(n) * A000010(n) = A051953(n),

a(n) * A000027(n) = A001065(n),

a(n) * A000012(n) = A032741(n).

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

Partial sums of A185012. - Jason Kimberley, Oct 15 2011

Decimal expansion of 1/900. - Elmo R. Oliveira, May 05 2024

LINKS

Table of n, a(n) for n=0..104.

J. S. Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g.

Index entries for linear recurrences with constant coefficients, signature (1).

FORMULA

a(n) = A057427(n-1) for n >= 2.

From Elmo R. Oliveira, Jul 20 2024: (Start)

G.f.: x^2/(1-x).

E.g.f.: exp(x) - x - 1. (End)

MATHEMATICA