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A164978 Number of divisors of n*(n+1)/2 that are >= n. 5
1, 1, 2, 2, 2, 2, 3, 4, 3, 2, 4, 4, 2, 4, 7, 4, 3, 3, 4, 7, 4, 2, 6, 8, 3, 4, 7, 4, 4, 4, 5, 9, 4, 4, 11, 6, 2, 4, 11, 6, 4, 4, 4, 11, 6, 2, 8, 11, 4, 6, 7, 4, 4, 7, 11, 11, 4, 2, 8, 8, 2, 6, 16, 11, 7, 4, 4, 7, 8, 4, 9, 9, 2, 6, 11, 8, 8, 4, 8, 18, 5, 2, 8, 15, 4, 4, 11, 6, 6, 11, 8, 7, 4, 4, 18, 10, 3, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) = 2 <=> the set S = {1..n} has only one decomposition into smaller subsets with equal element sum.

LINKS

Alois P. Heinz and T. D. Noe, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

FORMULA

a(n) = |{d|n*(n+1)/2 : d>=n}|.

EXAMPLE

a(6) = 2, because 6*7/2=21 with divisors {1,3,7,21}, but only 7 and 21 are >=6. S={1..6} has only one decomposition into smaller subsets with equal element sum: {1,6}, {2,5}, {3,4}.

a(7) = 3; 7*8/2=28 with divisors {1,2,4,7,14,28}, 3 of which are >=7. S={1..7} has 5 decompositions into smaller subsets with equal element sum.

MAPLE

with(numtheory):

a:= n-> nops(select(x-> x>=n, divisors(n*(n+1)/2))):

seq(a(n), n=1..120);

CROSSREFS

Cf. A164977, A035470.

Sequence in context: A262944 A322789 A069904 * A119789 A025424 A216505

Adjacent sequences:  A164975 A164976 A164977 * A164979 A164980 A164981

KEYWORD

easy,nonn

AUTHOR

Alois P. Heinz, Sep 03 2009

STATUS

approved

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Last modified August 21 18:38 EDT 2019. Contains 326168 sequences. (Running on oeis4.)