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

Author

Jaroslav Krizek, Sep 20 2013

Keywords

• nonn

Comments

Number of nonempty subsets of divisors of n = A100587(n).

Examples

			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).

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.