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A100007 Number of unitary divisors of 2n-1 (d such that d divides 2n-1, GCD(d,(2n-1)/d)=1). Bisection of A034444. 2
1, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 2, 4, 4, 2, 4, 2, 2, 4, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 2, 4, 2, 2, 4, 4, 2, 2, 2, 4, 4, 2, 4, 4, 4, 2, 4, 2, 2, 8, 2, 2, 4, 2, 4, 4, 4, 2, 4, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 4, 4, 2, 4, 4, 2, 8, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 8, 2, 2, 4, 4, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..105.

FORMULA

From Ilya Gutkovskiy, Apr 28 2017: (Start)

a(n) = [x^(2*n-1)] Sum_{k>=1} mu(k)^2*x^k/(1 - x^k).

a(n) = 2^omega(2*n-1). (End)

EXAMPLE

a(13)=2 because among the three divisors of 25 only 1 and 25 are unitary.

MAPLE

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

CROSSREFS

Cf. A034444.

Sequence in context: A083261 A003648 A003642 * A104369 A051702 A073130

Adjacent sequences:  A100004 A100005 A100006 * A100008 A100009 A100010

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 July 23 20:44 EDT 2019. Contains 325264 sequences. (Running on oeis4.)