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A100577 Number of sets of divisors of n with an odd sum. 2
1, 2, 2, 4, 2, 8, 2, 8, 4, 8, 2, 32, 2, 8, 8, 16, 2, 32, 2, 32, 8, 8, 2, 128, 4, 8, 8, 32, 2, 128, 2, 32, 8, 8, 8, 256, 2, 8, 8, 128, 2, 128, 2, 32, 32, 8, 2, 512, 4, 32, 8, 32, 2, 128, 8, 128, 8, 8, 2, 2048, 2, 8, 32, 64, 8, 128, 2, 32, 8, 128, 2, 2048, 2, 8, 32, 32, 8, 128, 2, 512, 16, 8, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = A000079(A032741(n)).

Also number of subsets of divisors of n which do not contain 1; thus a(n) = (A100587(n)+1)/2. - Vladeta Jovovic, Jul 02 2007

LINKS

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

FORMULA

a(n) = 2^(A000005(n)-1).

EXAMPLE

a(12) = #{{1}, {3}, {1,2}, {1,4}, {2,3}, {1,6}, {3,4}, {1,2,4}, {3,6}, {1,2,6}, {2,3,4}, {1,4,6}, {2,3,6}, {1,12}, {3,4,6}, {1,2,4,6}, {3,12}, {1,2,12}, {2,3,4,6}, {1,4,12}, {2,3,12}, {1,6,12}, {3,4,12}, {1,2,4,12}, {3,6,12}, {1,2,6,12}, {2,3,4,12}, {1,4,6,12}, {2,3,6,12}, {1,2,4,6,12}, {3,4,6,12}, {2,3,4,6,12}} = 32.

MAPLE

A100577 := proc(n)

    2^(numtheory[tau](n)-1) ;

end proc:

seq(A100577(n), n=1..100) ; # R. J. Mathar, Nov 10 2017

PROG

(PARI) a(n)=2^(numdiv(n)-1) \\ Charles R Greathouse IV, Jan 19 2017

CROSSREFS

Cf. A000005, A000079, A001227, A032741, A100587.

Sequence in context: A270366 A072478 A190014 * A018818 A157019 A067538

Adjacent sequences:  A100574 A100575 A100576 * A100578 A100579 A100580

KEYWORD

nonn,easy,changed

AUTHOR

Reinhard Zumkeller, Nov 29 2004

STATUS

approved

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Last modified November 18 09:09 EST 2017. Contains 294879 sequences.