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A141218
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Write the n-th nonprime (A018252(n)) as a product of primes; decrease one copy of the largest prime by 1 and increase one copy of the smallest prime by 1, multiply the resulting numbers.
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6
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1, 3, 6, 6, 8, 12, 12, 18, 16, 12, 18, 24, 24, 30, 24, 24, 36, 24, 36, 36, 24, 40, 48, 36, 36, 54, 48, 48, 54, 60, 48, 66, 48, 48, 60, 64, 72, 54, 60, 72, 72, 84, 72, 90, 72, 48, 72, 90, 96, 88, 90, 72, 108, 80, 108, 80, 108, 96, 72, 120, 108, 96, 126, 112, 120, 108, 96, 132, 120
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OFFSET
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1,2
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LINKS
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EXAMPLE
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1st nonprime = 1 (has no prime factors); a(1) = empty product = 1.
2nd nonprime = 4 = (p(max)=2)*(p(min)=2); a(2) = (2-1)*(2+1) = 1*3 = 3.
3rd nonprime = 6 = (p(max)=3)*(p(min)=2); a(3) = (3-1)*(2+1) = 2*3 = 6.
4th nonprime = 8 = (p(max)=2)*(p=2)*(p(min)=2); a(4) = (2-1)*2*(2+1) = 1*2*3 = 6.
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MAPLE
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f:= proc(m) local F, p1, p2;
if isprime(m) then return NULL fi;
F:= numtheory:-factorset(m);
p1:= min(F); p2:= max(F);
m*(p1+1)/p1*(p2-1)/p2;
end proc:
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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