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

1,2

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

Mathematica

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

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: A190014 A353214 A350062 * A328710 A018818 A157019

Adjacent sequences: A100574 A100575 A100576 * A100578 A100579 A100580

Keyword

nonn,easy

Author

Reinhard Zumkeller, Nov 29 2004

Status

approved