A190938 Parity of the multiplicative partition function A001055.

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

Offset

1

Comments

Suggested by the title of a talk by Paul Pollack in the program for the 2011 Illinois Number Theory Conference.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Paul Pollack, The parity of the multiplicative partition function, Talk at 2011 Illinois number theory meeting.

Paul Pollack, On the parity of the number of multiplicative partitions and related problems, Proc. Amer. Math. Soc. 140 (2012), 3793-3803.

A. Zaharescu and M. Zaki, On the parity of the number of multiplicative partitions, Acta Arith. 145 (2010), no. 3, 221-232. MR2733086. doi: 10.4064/aa145-3-2.

Formula

a(n) = A001055(n) mod 2.

Prog

(PARI) fcnt(n, m) = {local(s); s=0; if(n == 1, s=1, fordiv(n, d, if(d > 1 & d <= m, s=s+fcnt(n/d, d)))); s}
vector(100, n, fcnt(n, n) % 2) \\ after Michael B. Porter in A001055, Michel Marcus, Jun 21 2015

Crossrefs

Cf. A001055, A040051.

Sequence in context: A354034 A174897 A316441 * A342653 A189166 A092079

Adjacent sequences: A190935 A190936 A190937 * A190939 A190940 A190941

Keyword

nonn

Author

N. J. A. Sloane, May 24 2011

Status

approved