A229337 Sum of products of elements of nonempty subsets of divisors of n.

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).

Links

Table of n, a(n) for n=1..46.

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

Adjacent sequences: A229334 A229335 A229336 * A229338 A229339 A229340

Keyword

nonn

Author

Jaroslav Krizek, Sep 20 2013

Status

approved