A145377 a(n) = A002324(n) mod 2.

1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

N. J. A. Sloane, Mar 12 2009

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• J. S. Rutherford, Generating functions for the cage isomers of the C_{20n} icosahedral fullerenes, J. Mathematical Chem., 14 (1993), 385-390. See Eq. (3).
• J. S. Rutherford, The enumeration and symmetry-significant properties of derivative lattices, Act. Cryst. A48 (1992), 500-508. [See Sect. (7), p. 505.]
• Index entries for characteristic functions

Crossrefs

Essentially same as A195198.

Cf. A002324, A154272, A003050.

Programs

Mathematica

Array[Boole@ OddQ@ If[# < 1, 0, DivisorSum[#, KroneckerSymbol[-3, #] &]] &, 105] (* Michael De Vlieger, Nov 05 2017, after Michael Somos at A002324 *)

PARI

A002324(n) = if( n<1, 0, sumdiv(n, d, (d%3==1) - (d%3==2)));
A145377(n) = (A002324(n)%2); \\ Antti Karttunen, Nov 06 2017

Formula

a(n) = A195198(n) for n >= 1.

a(n) = Sum_{ m: m^2|n } A154272(n/m^2). - Andrey Zabolotskiy, May 07 2018

Extensions

More terms from Antti Karttunen, Nov 05 2017