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A088075
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Smallest number sandwiched between two numbers having exactly n prime divisors.
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2
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3, 11, 131, 1429, 77141, 1456729, 117048931, 10326137821, 1110819807371, 140734085123059, 11639258217451019
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OFFSET
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1,1
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COMMENTS
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a(n)=m is the smallest number sandwiched between m-1 and m+1 such that both m+1 and m-1 have n distinct prime-factors. No restrictions are imposed for {m-1,m+1} flanker numbers.
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REFERENCES
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Jean-Marie De Koninck, "Those Fascinating Numbers", American Mathematical Society, 2009, entry 1428. (This gives the lower of the two numbers.)
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LINKS
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FORMULA
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EXAMPLE
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n = 3: a(3) = 131, 130 = 2*5*13 and 132 = 2^2*3*11 both have three prime divisors.
n = 6: a(6) = 1456729 = 103*14143 is between 1456728 = 8*3*7*13*23*29 and 1456730 = 2*5*11*17*19*41.
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PROG
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(PARI) isok(k, n) = (omega(k-1)==n) && (omega(k+1)==n);
a(n) = my(k=2); while (!isok(k, n), k++); k; \\ Michel Marcus, Sep 03 2023
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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