A100577 Number of sets of divisors of n with an odd sum.

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

Offset: 1

Author

Reinhard Zumkeller, Nov 29 2004

Keywords

• nonn
• easy

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Maple

A100577 := proc(n)
    2^(numtheory[tau](n)-1) ;
end proc:
seq(A100577(n),n=1..100) ; # R. J. Mathar, Nov 10 2017

Mathematica

Table[2^(DivisorSigma[0, n] - 1), {n, 1, 100}] (* Jean-François Alcover, Feb 13 2018 *)

PARI

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

Formula

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