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A229337
Sum of products of elements of nonempty subsets of divisors of n.
3
1, 5, 7, 29, 11, 167, 15, 269, 79, 395, 23, 10919, 27, 719, 767, 4589, 35, 31919, 39, 41579, 1407, 1655, 47, 2456999, 311, 2267, 2239, 104399, 59, 5499647, 63, 151469, 3263, 3779, 3455, 76767599, 75, 4679, 4479, 15343019, 83, 19071359, 87, 372599, 353279, 6767
OFFSET
1,2
COMMENTS
Number of nonempty subsets of divisors of n = A100587(n).
FORMULA
Let a, b, c, ..., k be all divisors of n; a(n) = (a+1) * (b+1) * ... * (k+1) - 1.
a(p) = 2p+1, a(p^2) = 2(p+1)(p^2+1) - 1.
a(n) = A020696(n) - 1.
EXAMPLE
For n = 2^2 = 4; divisors of 4: {1, 2, 4}; nonempty subsets of divisors of n: {1}, {2}, {4}, {1, 2}, {1, 4}, {2, 4}, {1, 2, 4}; sum of products of elements of subsets = 1 + 2 + 4 + 2 + 4 + 8 + 8 = 29 = (1+1) * (2+1) * (4+1) - 1.
CROSSREFS
Cf. A229335 (sum of sums of elements of nonempty subsets of divisors of n), A229336 (product of sums of elements of nonempty subsets of divisors of n), A229338 (product of products of elements of nonempty subsets of divisors of n).
Sequence in context: A185302 A179305 A307100 * A227857 A266078 A147993
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Sep 20 2013
STATUS
approved