

A112343


Positive integers n such that the largest primepower divisor of n equals the sum of the other largest primepowers (>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, pn} p^k(p), each k(p) = positive integer, then sum{p=primes, pn} p^k(p) = twice the largest prime power dividing n. The inclusion of 1 in the sequence is debatable.


LINKS

Table of n, a(n) for n=1..46.


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

Cf. A034699, A008475.
Sequence in context: A270758 A241192 A064623 * A182996 A325378 A164596
Adjacent sequences: A112340 A112341 A112342 * A112344 A112345 A112346


KEYWORD

nonn


AUTHOR

Leroy Quet, Dec 01 2005


EXTENSIONS

Edited by Ray Chandler, Dec 04 2005


STATUS

approved



