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A055233
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Composite numbers equal to the sum of the primes from their smallest prime factor to their largest prime factor.
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11
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OFFSET
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1,1
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COMMENTS
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Composite n such that n = p_1 + p_2 + ... + p_k where the p_i are consecutive primes, p_1 is the smallest prime factor of n and p_k is the largest.
Concerning a(6): 454539357304421 is the product of two primes, 3536123 * 128541727 and also the sum of these two plus all the primes in between: 3536123 + 3536129 + 3536131 + ... + 128541719 + 128541727. I do not know if there are any terms in A055233 between 2935561623745 and 454539357304421. (I have searched for values of N satisfying N=Pa*Pb=Pa+...+Pb as far as 5.98*10^16, but this is not quite the same as A055233 or A055514.) - Robert Munafo, Nov 20 2002
This is a subsequence of A055514 where the sum must be divisible by the smallest and largest term, but they need not be its smallest and largest prime factor. Without restriction to composite numbers, all primes would be trivially included: see A169802. - M. F. Hasler, Nov 21 2021
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LINKS
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EXAMPLE
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10 = 2*5 = 2 + 3 + 5;
39 = 3*13 = 3 + 5 + 7 + 11 + 13;
371 = 7*53 = 7 + 11 + 13 + ... + 53.
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MATHEMATICA
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Select[Range[2, 10^3], And[CompositeQ@ #1, #1 == #2] & @@ {#, Total@ Prime[Range @@ PrimePi@ {#[[1, 1]], #[[-1, 1]]} &@ FactorInteger[#]]} &] (* Michael De Vlieger, Sep 04 2019 *)
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CROSSREFS
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Cf. A020639 (spf: smallest prime factor), A006530 (gpf: greatest prime factor).
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KEYWORD
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nice,nonn
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AUTHOR
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EXTENSIONS
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454539357304421 confirmed to be the 6th term by Donovan Johnson, Aug 23 2010
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STATUS
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approved
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