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A190938 Parity of the multiplicative partition function A001055. 10
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 (list; graph; refs; listen; history; text; internal format)
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: A132194 A174897 A316441 * A189166 A092079 A140074

Adjacent sequences:  A190935 A190936 A190937 * A190939 A190940 A190941

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 24 2011

STATUS

approved

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Last modified March 19 15:02 EDT 2019. Contains 321330 sequences. (Running on oeis4.)