A220848 a(n) = sum_(d|n) product_(d_x|n, d_x<=d) d_x.

1, 3, 4, 11, 6, 45, 8, 75, 31, 113, 12, 1905, 14, 213, 244, 1099, 18, 6201, 20, 8451, 466, 509, 24, 346929, 131, 705, 760, 22803, 30, 839019, 32, 33867, 1126, 1193, 1266, 10374657, 38, 1485, 1564, 2627571, 42, 3189609, 44, 87219, 93304, 2165, 48, 260348721

Offset

1,2

Comments

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

The conjecture is true for the first 100000 terms. - Harvey P. Dale, Dec 02 2017

Links

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

Formula

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

Example

The divisors of 6 are 1, 2, 3, 6. a(n) = 1 + (1*2) + (1*2*3) + (1*2*3*6) = 1 + 2 + 6 + 36 = 45.

Mathematica

f[x_]:=Module[{d=Divisors[x]}, Total[Table[Times@@Take[d, n], {n, Length[ d]}]]]; Array[f, 50] (* Harvey P. Dale, Dec 02 2017 *)

Crossrefs

Sequence in context: A175317 A056045 A360794 * A370605 A232891 A096223

Adjacent sequences: A220845 A220846 A220847 * A220849 A220850 A220851

Keyword

nonn,easy

Author

Jaroslav Krizek, Dec 22 2012

Status

approved