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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

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

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Last modified July 15 02:31 EDT 2020. Contains 335762 sequences. (Running on oeis4.)