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A064355 Number of subsets of {1,2,..n} that sum to 1 mod n. 3
2, 2, 2, 4, 6, 10, 18, 32, 56, 102, 186, 340, 630, 1170, 2182, 4096, 7710, 14560, 27594, 52428, 99858, 190650, 364722, 699040, 1342176, 2581110, 4971008, 9586980, 18512790, 35791358, 69273666, 134217728, 260300986, 505290270, 981706806 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..35.

Index entries for sequences related to subset sums modulo m

FORMULA

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).

EXAMPLE

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}.

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A010558 A060827 A188288 * A000799 A185030 A063823

Adjacent sequences:  A064352 A064353 A064354 * A064356 A064357 A064358

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

More terms from Vladeta Jovovic, Sep 27 2001

STATUS

approved

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Last modified January 23 02:57 EST 2019. Contains 319368 sequences. (Running on oeis4.)