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A100008 Number of unitary divisors of 2n. 1
2, 2, 4, 2, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 8, 2, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 2, 8, 4, 8, 4, 4, 4, 8, 4, 4, 8, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 8, 4, 8, 4, 4, 8, 4, 4, 8, 2, 8, 8, 4, 4, 8, 8, 4, 4, 4, 4, 8, 4, 8, 8, 4, 4, 4, 4, 4, 8, 8, 4, 8, 4, 4, 8, 8, 4, 8, 4, 8, 4, 4, 4, 8, 4, 4, 8, 4, 4, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

b(n) = a(n)/a(1) is multiplicative with b(2^e) = 1, b(p^e) = 2 otherwise. - David W. Wilson, Jun 12 2005

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A000079(A099812(n)) = A000079(A001221(2n)) = 2*A068068(n). - Antti Karttunen, Sep 14 2017

EXAMPLE

a(6)=4 because among the six divisors of 12 only 1,3,4 and 12 are unitary.

MAPLE

with(numtheory): for n from 1 to 120 do printf(`%d, `, 2^nops(ifactors(2*n)[2])) od: # Emeric Deutsch, Dec 24 2004

PROG

(PARI) A100008(n) = 2^omega(2*n); \\ Antti Karttunen, Sep 14 2017

CROSSREFS

Bisection of A034444, twice A068068.

Cf. A000079, A001221, A099812.

Sequence in context: A091248 A082991 A214212 * A102763 A054844 A057936

Adjacent sequences:  A100005 A100006 A100007 * A100009 A100010 A100011

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 20 2004

EXTENSIONS

More terms from Emeric Deutsch, Dec 24 2004

STATUS

approved

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Last modified June 20 00:47 EDT 2019. Contains 324223 sequences. (Running on oeis4.)