login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A112343 Positive integers n such that the largest prime-power divisor of n equals the sum of the other largest prime-powers (>1) dividing n. 0
1, 30, 70, 84, 120, 126, 180, 198, 264, 286, 308, 468, 520, 624, 646, 880, 884, 912, 1008, 1150, 1224, 1350, 1566, 1672, 1748, 1798, 2484, 2576, 2784, 2900, 3135, 3348, 3400, 3526, 3570, 3600, 4104, 4320, 4606, 4752, 5600, 5704, 5920, 6032, 6068, 6279 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Sequence consists of those positive integers n where, if n = product{p=primes, p|n} p^k(p), each k(p) = positive integer, then sum{p=primes, p|n} p^k(p) = twice the largest prime power dividing n. The inclusion of 1 in the sequence is debatable.
LINKS
EXAMPLE
84 = 2^2 * 3 * 7. Now 7 = 2^2 + 3. So 84 is in the sequence.
120 = 2^3 * 3 * 5. Now 2^3 = 3 + 5, so 120 is in the sequence.
MATHEMATICA
f[n_] := Block[{pp}, If[n == 1, Return[True]]; pp = Power @@@ FactorInteger[n]; Return[2Max[pp] == Plus @@ pp]; ]; Select[Range[6500], f] (* Ray Chandler, Dec 04 2005 *)
CROSSREFS
Sequence in context: A241192 A359545 A064623 * A182996 A325378 A164596
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 01 2005
EXTENSIONS
Edited by Ray Chandler, Dec 04 2005
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)