A050214 a(n) = Product_{d|n, d^2<=n} (d+n/d); a(1)=1.

1, 3, 4, 20, 6, 35, 8, 54, 60, 77, 12, 728, 14, 135, 128, 1360, 18, 1881, 20, 2268, 220, 299, 24, 38500, 260, 405, 336, 5104, 30, 75361, 32, 7128, 476, 665, 432, 1731600, 38, 819, 640, 164164, 42, 218569, 44, 16200, 11592, 1175, 48, 5422144, 700, 20655, 1040

Offset

1,2

Comments

a(n) = n+1 iff n is prime.

Links

Table of n, a(n) for n=1..51.

Example

a(12) = (1+12)*(2+6)*(3+4) = 13*8*7 = 728.

Mathematica

pdn[n_]:=Module[{d=Select[Divisors[n], #^2<=n&]}, Times@@ (Total/@ ({#, n/#}&/@d ))]; Join[{1}, Array[pdn, 60, 2]] (* Harvey P. Dale, May 03 2013 *)

Crossrefs

Sequence in context: A041989 A196198 A041561 * A256605 A237884 A256532

Adjacent sequences: A050211 A050212 A050213 * A050215 A050216 A050217

Keyword

nonn

Author

Reinhard Zumkeller, May 08 2003

Extensions

Corrected and extended by Harvey P. Dale, May 03 2013

Status

approved