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A100577
Number of sets of divisors of n with an odd sum.
5
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
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
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Nov 29 2004
STATUS
approved