A220846 a(n) = sum_(d|n) ((product_(d|n) d) / d).

1, 3, 4, 14, 6, 72, 8, 120, 39, 180, 12, 4032, 14, 336, 360, 1984, 18, 12636, 20, 16800, 672, 792, 24, 829440, 155, 1092, 1080, 43904, 30, 1944000, 32, 64512, 1584, 1836, 1680, 25474176, 38, 2280, 2184, 5760000, 42, 7112448, 44, 162624, 157950, 3312, 48

Offset

1,2

Comments

Conjecture: sequence is injective (all terms of this sequence occur exactly once).

Links

Jaroslav Krizek, Table of n, a(n) for n = 1..100

Formula

a(n) = sum_(d|n) (A007955(n) / d).

a(p) = p + 1 for prime p.

Example

The divisors of 6 are 1, 2, 3, 6. A007955(6) = product_(d|6) d = 1*2*3*6 = 36.
a(6) = 36/1 + 36/2 + 36/3 + 36/6 = 36 + 18 + 12 + 6 = 72.

Crossrefs

Cf. A007955 (product of divisors of n.).

Sequence in context: A082732 A307893 A337297 * A009286 A076663 A277933

Adjacent sequences: A220843 A220844 A220845 * A220847 A220848 A220849

Keyword

nonn

Author

Jaroslav Krizek, Dec 22 2012

Status

approved