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A333646
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Numbers k divisible by the largest prime factor of the sum of divisors of k; a(1) = 1.
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3
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1, 6, 15, 28, 30, 33, 40, 42, 51, 66, 69, 84, 91, 95, 102, 105, 117, 120, 135, 138, 140, 141, 145, 159, 165, 182, 186, 190, 210, 213, 224, 231, 234, 255, 270, 273, 280, 282, 285, 287, 290, 295, 308, 318, 321, 330, 345, 357, 364, 395, 420, 426, 435, 440, 445, 455
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OFFSET
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1,2
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COMMENTS
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Pomerance (1973) proved that all the harmonic numbers (A001599) are in this sequence.
If m is a product of distinct Mersenne primes (A046528), m > 1 and 3 | m, then 2*m is a term.
If p is a term of A005105 then, 6*p is a term for p > 3, and 3*p is a term if p is not a Mersenne prime (A000668).
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LINKS
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Carl Pomerance, On a Problem of Ore: Harmonic Numbers, unpublished manuscript, 1973; abstract *709-A5, Notices of the American Mathematical Society, Vol. 20, 1973, page A-648, entire volume.
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FORMULA
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Numbers k such that A071190(k) | k.
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EXAMPLE
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15 is a term since sigma(15) = 24, 3 is the largest prime factor of 24, and 15 is divisible by 3.
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MATHEMATICA
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Select[Range[500], Divisible[#, FactorInteger[DivisorSigma[1, #]][[-1, 1]]] &]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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