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Search: id:A112343
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| A112343 |
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Positive integers n such that the largest prime-power divisor of n equals the sum of the other largest prime-powers (>1) dividing n. |
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+0
1
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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.
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EXAMPLE
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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.
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MATHEMATICA
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f[n_] := Block[{pp}, If[n == 1, Return[True]]; pp = Power @@@ FactorInteger[n]; Return[2Max[pp] == Plus @@ pp]; ]; Select[Range[6500], f] (*Chandler*)
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CROSSREFS
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Cf. A034699, A008475.
Sequence in context: A044132 A044513 A064623 this_sequence A131647 A071141 A071312
Adjacent sequences: A112340 A112341 A112342 this_sequence A112344 A112345 A112346
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Dec 01 2005
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EXTENSIONS
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Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 04 2005
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