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Search: id:A055233
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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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+0
5
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OFFSET
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0,1
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COMMENT
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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.
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LINKS
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C. Rivera, Puzzle
Robert Munafo, Notable Properties of Specific Numbers
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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.
503 + 509 + 521 + ... + 508203 = 10225245560, which is divisible by 503 and 508203
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CROSSREFS
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Cf. A055514.
Sequence in context: A059722 A074225 A055514 this_sequence A104045 A102546 A108777
Adjacent sequences: A055230 A055231 A055232 this_sequence A055234 A055235 A055236
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KEYWORD
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nice,nonn
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AUTHOR
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Carlos B. Rivera F (crivera(AT)primepuzzles.net), Jun 21 2000
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EXTENSIONS
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a(5) found by Jud McCranie (j.mccranie(AT)comcast.net), Jul 03 2000
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 A0055233 or A055514.) - Robert P. Munafo (mrob(AT)mrob.com), Nov 20 2002
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