1,1

Index entries for sequences related to subset sums modulo m

a(n) = 1/n * sum_{d divides n and d is odd} 2^(n/d) * mu(d); (mu(d) is the Moebius function, sequence A008683).

a(7)=18 because there are 18 subsets of {1,2,3,4,5,6,7} which sum to 1 mod 7:{1}, {1,7}, {2,6}, {3,5}, {1,2,5}, {1,3,4}, {2,6,7}, {3,5,7}, {4,5,6}, {1,2,5,7}, {1,3,4,7}, {1,3,5,6}, {2,3,4,6}, {4,5,6,7}, {1,2,3,4,5}, {1,3,5,6,7}, {2,3,4,6,7}, {1,2,3,4,5,7}.

f[n_] := Block[{d = Select[Divisors@n, OddQ@ # &]}, Plus @@ (2^(n/d)*MoebiusMu@d)/n]; Array[f, 35] (from Robert G. Wilson v (rgwv(at)rgwv.com), Feb 20 2006)

Cf. A063776, A008683. Equals 2*A000048(n).

Sequence in context: A036654 A010558 A060827 this_sequence A000799 A063823 A005865

Adjacent sequences: A064352 A064353 A064354 this_sequence A064356 A064357 A064358

nonn

Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Sep 25 2001

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 27 2001